climactic limitation of alien weeds in new zealand: enhancing

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thesis.

Climatic Limitation of Alien

Weeds in New Zealand:

Enhancing Species Distribution

Models with Field Data

A thesis

submitted in partial fulfilment

of the requirements for the Degree of

Doctor of Philosophy

at

Lincoln University

by

Jennifer L. Pannell

Lincoln University

2016

ii

“...think of a blossom in a painting rendered photographic in detail and as

beautiful as life. In our minds the macroscopic entity has truth because it

matches real flowers sprung from the soil. From a distance we might easily

confuse the image with the real thing. But the algorithms that created it are

radically different. Its microscopic elements are flakes of paint instead of

chromosomes and cells. Its developmental pathways exist in the brain of the

artist, not in prescription by DNA of the unfolding of tissues. How do

theoreticians know that their computer simulations are not just the paintings

of flowers?”

– Edward O. Wilson, “Consilience”

iii

Abstract

Correlative species distribution models (SDMs) are often used to quantify the potential ranges of alien

species. Despite rising popularity, there is ongoing debate surrounding whether SDMs can predict

non-equilibrium species, how well they capture underlying biological mechanisms versus drawing

spurious correlations, and how realistic the ensuing projections are. There have been numerous calls to

integrate SDMs with real-world performance data to validate and improve projections, but such

studies remain rare. In this thesis, I investigated the potential distributions of three alien plant species,

Aeonium arboreum, A. haworthii and Cotyledon orbiculata, in their introduced ranges of New

Zealand. I used a combination of SDMs, observational and experimental approaches. I firstly

developed correlative SDMs for the three species. Secondly, I quantified the species’ climatic limits in

the study region of Banks Peninsula, New Zealand, using field transplant experiments and surveys.

Finally, I combined the aforementioned plant performance data into a single climate-driven population

model, which I used to test and enhance the original SDM projections. I found that the New Zealand

distributions of all three species are climatically novel relative to their distributions elsewhere, and

constitute shifts in their realized niches. Although SDMs indicated that much of New Zealand is

climatically suitable, transplant experiments on Banks Peninsula confirmed that the climate of Banks

Peninsula is limiting. In all three species, low growth rates, low germination, and high mortality at

high elevations will limit spread. In contrast, surveys found little evidence of direct climatic limitation

to fecundity within the species’ current distributions on Banks Peninsula. The final step of validating

SDM projections against the population model revealed that the SDM performed better than k-folds

cross-validation against occurrence data would suggest. However, the SDMs over-predicted suitable

climate in the region. I therefore adjusted SDM thresholds of modelled suitability to optimise

parsimony with field data and provide more robust projections for Banks Peninsula. This is the first

thorough study of climatic limitation of the target species. It is also one of few to experimentally test

SDMs and use field performance data to enhance projections. Although I found support for the

usefulness of SDMs, the results emphasise the need for scepticism and rigorous testing of outputs.

Validating SDMs against field data was highly effective, and was a better test of model performance

than conventional methods using occurrence data. Uptake of similar methods as outlined in this thesis

would improve understanding of uncertainty in distribution modelling. I encourage the use of such

techniques not only for improving confidence in model projections, but also in recognizing the relative

impact of sources of error in our models. At a time when generating projections of species’ potential

distributions has never been easier, the need for considered judgements in SDM building and cautious

interpretation of outputs is emphasised by my findings.

Keywords: climate, Crassulaceae, elevation, equilibrium, fecundity, germination, growth, invasions,

IPMs, mortality, New Zealand, niche, performance, population model, SDMs, validation.

iv

Acknowledgements

I am thankful for the guidance, support and patience of my supervisory team, Professor Phil Hulme,

Professor Richard Duncan and Associate Professor Sue Worner. Their collective wisdom has been

invaluable and I have been consistently pushed to develop my modelling, statistical and writing skills.

I am also grateful for the chance to collaborate with Dr Darren Kriticos, whose advice tranformed my

distribution modelling work, and was extremely helpful in the development and writing of Chapter 2.

I would also like to thank the many people who gave technical and field assistance during my long

field seasons. I could not have hoped to do such an extensive field project alone.

Field surveys: I thank, in no particular order, my field assistants Haylee Wen See Lim, Amy McCulla,

Corrine Staley, Robyn Butters, Kelly Murray, Lynda Doherty, Kenny Perry, and Ruaire Murray. I

particularly thank those who gave up their days off to help me measure plants, despite not being the

slightest bit interested in ecology, and who asked for nothing in return except perhaps lunch and a cold

beer afterwards.

Experiments and lab work: I thank my field assistants Jagoba Malumbres-Olarte, Kirsty McGregor,

Aimee McCulla, Katie Villano, and Ruaire Murray. I am especially grateful for being able to rely on

Robyn Butters throughout my field work, only through her hard work was it possible to get such a

large experiment completed. I also thank the Lincoln University Field Services Centre and Nursery, in

particular Dan Dash for giving up his time to help me dig holes on hillsides. I also benefitted greatly

from the knowledge of Maria-Elena Duter and the facilities of the Lincoln University Seed Research

Centre. Perhaps most of all, I thank Di Carter and the Port Hills Rangers for their interest in the project

and their ongoing assistance, for allowing the use of council reserves, and for practical help with

removal of plant material. The field experiment was carried out under permits granted by Christchurch

City Council, Environment Canterbury (ECan) and the Ministry for Primary Industries (MPI).

I have been lucky to be surrounded by many fantastic colleagues during my time in Lincoln. I thank

Elizabeth Wandrag, Kirsty McGregor, Federico Tomasetto, Tyler Brummer, Samuel Tourtellot,

Andreas Makiola, Tasha Shelby, Kevin McGinn, Senait Senay and Audrey Lustig for their moral and

technical support. I also thank Makihiko Ikegami and Will Godsoe for their constructive feedback, and

Jennifer Bufford for the crash course in integral projection models. Lastly, I would like to thank the

wonderful people who helped keep me sane and grounded during my PhD studies, especially Sinead

Carragher, Bridget Rowe and Tara Welham for being extremely good at pretending to be interested in

my science rants. I thank my parents Lesley and Nick Pannell, and sisters Liz Barrett and Claire Gray,

for their unconditional support. Finally, thanks to my fiancé Ruaire Murray, for being my personal

cheerleader, unofficial research assistant and sounding board over the past few years, and for helping

me remember, every time, where I left that very important post-it note.

v

Table of contents

Abstract ................................................................................................................................................. iii

Acknowledgements ................................................................................................................................ iv

Table of contents .................................................................................................................................... v

List of tables ........................................................................................................................................... ix

List of figures ....................................................................................................................................... xii

Chapter 1 - Introduction........................................................................................................................ 1

1.1 Spatial ecology – the where and why of invasions ........................................................................ 1

1.2 Making models of reality ............................................................................................................... 2 1.2.1 Correlative SDMs ............................................................................................................. 3 1.2.2 When SDMs go awry ........................................................................................................ 5 1.2.3 Complementing SDMs with real-world data .................................................................... 5 1.2.4 Structure of thesis .............................................................................................................. 6

1.3 Alien Crassulaceae of New Zealand .............................................................................................. 7 1.3.1 Selecting three study species ............................................................................................. 7 1.3.2 Banks Peninsula .............................................................................................................. 10

1.4 Thesis objectives .......................................................................................................................... 12

1.5 Thesis style................................................................................................................................... 12

Chapter 2 – Modelling the global and New Zealand niches of alien Crassulaceae indicates

invasion of novel climates .................................................................................................................... 13

2.1 Abstract ........................................................................................................................................ 13

2.2 Introduction .................................................................................................................................. 13 2.2.1 Aims ................................................................................................................................ 16

2.3 Methods ....................................................................................................................................... 16 2.3.1 Study species ................................................................................................................... 16 2.3.2 Distribution data .............................................................................................................. 17 2.3.3 Environmental variables ................................................................................................. 19 2.3.4 Niche analysis ................................................................................................................. 19 2.3.5 Model of climate suitability ............................................................................................ 20 2.3.6 A priori non-climatic constraints .................................................................................... 21 2.3.7 Land use constraints for C. orbiculata ............................................................................ 22 2.3.8 Model verification ........................................................................................................... 24

2.4 Results .......................................................................................................................................... 25 2.4.1 Niche analyses ................................................................................................................. 25 2.4.2 Performance of BIOCLIM models .................................................................................. 27 2.4.3 New Zealand projections and habitat suitability ............................................................. 29

2.5 Discussion .................................................................................................................................... 33 2.5.1 What do the models reveal about the niche? ................................................................... 33 2.5.2 The role of non-climatic factors ...................................................................................... 34 2.5.3 Potential distributions in New Zealand ........................................................................... 35 2.5.4 Limitations ...................................................................................................................... 36 2.5.5 Conclusions ..................................................................................................................... 37

vi

Chapter 3 – Testing performance along an elevation gradient reveals the climatic limits of

alien Crassulaceae in New Zealand .................................................................................................... 38

3.1 Abstract ........................................................................................................................................ 38


3.3 Methods ....................................................................................................................................... 41 3.3.1 Study species ................................................................................................................... 41 3.3.2 Study area ........................................................................................................................ 42 3.3.3 Experimental design ........................................................................................................ 42 3.3.4 Growth and mortality experiment ................................................................................... 43 3.3.5 Germination and seedling survival experiment ............................................................... 46 3.3.6 Risk mitigation and site monitoring ................................................................................ 47 3.3.7 Analysis and environmental variables ............................................................................ 47 3.3.8 Model fitting and performance ........................................................................................ 48 3.3.9 Comparison with observed distribution .......................................................................... 49 3.3.10 Sources of uncertainty ..................................................................................................... 50

3.4 Results .......................................................................................................................................... 51 3.4.1 Seedling establishment .................................................................................................... 51 3.4.2 Annual relative growth .................................................................................................... 51 3.4.3 Mortality.......................................................................................................................... 56 3.4.4 Elevation limits on Banks Peninsula ............................................................................... 57

3.5 Discussion .................................................................................................................................... 61 3.5.1 Predicted limits ............................................................................................................... 61 3.5.2 Climatic drivers ............................................................................................................... 62 3.5.3 Implications for Banks Peninsula.................................................................................... 64 3.5.4 Limitations ...................................................................................................................... 65 3.5.5 Conclusions ..................................................................................................................... 65

Chapter 4 – Exploring the link between fecundity and climate in naturalized populations of

alien Crassulaceae ................................................................................................................................ 66

4.1 Abstract ........................................................................................................................................ 66


4.3 Methods ....................................................................................................................................... 68 4.3.1 Study species ................................................................................................................... 68 4.3.2 Study area ........................................................................................................................ 69 4.3.3 Flowering surveys ........................................................................................................... 70 4.3.4 Seed counts ..................................................................................................................... 72 4.3.5 Climate variables ............................................................................................................. 73 4.3.6 Model fitting ................................................................................................................... 74 4.3.7 Model predictions ........................................................................................................... 75

4.4 Results .......................................................................................................................................... 76 4.4.1 General patterns .............................................................................................................. 76 4.4.2 Flowering probability ...................................................................................................... 76 4.4.3 Inflorescences per plant .................................................................................................. 79 4.4.4 Flowers per inflorescence ............................................................................................... 79 4.4.5 Seed production ............................................................................................................... 81 4.4.6 Site differences in canopy volume .................................................................................. 83 4.4.7 Total per capita fecundity................................................................................................ 84

4.5 Discussion .................................................................................................................................... 85 4.5.1 Direct climate limitation ................................................................................................. 85 4.5.2 Plant size – indirect climate limitation? .......................................................................... 86 4.5.3 Implications for spread, and limitations .......................................................................... 87 4.5.4 Conclusions ..................................................................................................................... 88

vii

Chapter 5 – Validating SDM projections against field data ............................................................ 90

5.1 Abstract ........................................................................................................................................ 90


5.3 Methods ....................................................................................................................................... 94 5.3.1 Study species ................................................................................................................... 94 5.3.2 Study area ........................................................................................................................ 94 5.3.3 Integral projection models............................................................................................... 95 5.3.4 Climate variables ............................................................................................................. 96 5.3.5 IPM parameters ............................................................................................................... 97 5.3.6 IPM structure................................................................................................................... 99 5.3.7 Verification of IPMs ..................................................................................................... 100 5.3.8 Validation of BIOCLIM projections ............................................................................. 101 5.3.9 Improving BIOCLIM projections ................................................................................. 102

5.4 Results ........................................................................................................................................ 102 5.4.1 IPM predictions ............................................................................................................. 102 5.4.2 Perturbation analyses .................................................................................................... 105 5.4.3 Validation of BIOCLIM projections ............................................................................. 105 5.4.4 Can BIOCLIM distinguish fundamental presences from absences? ............................. 106 5.4.5 Improving BIOCLIM projections for Banks Peninsula ................................................ 110

5.5 Discussion .................................................................................................................................. 112 5.5.1 Accuracy of IPM and BIOCLIM projections ................................................................ 112 5.5.2 Why did BIOCLIM over-predict suitable climate?....................................................... 113 5.5.3 Limitations .................................................................................................................... 115 5.5.4 Conclusions ................................................................................................................... 116

Chapter 6 - General discussion ......................................................................................................... 117

6.1 Summary of findings .................................................................................................................. 117

6.2 Species distribution models vs. reality ....................................................................................... 118 6.2.1 How well did SDMs predict plant performance? .......................................................... 118 6.2.2 Improving SDM accuracy ............................................................................................. 119

6.3 The future of non-native Crassulaceae on Banks Peninsula ...................................................... 120 6.3.1 Climatic limitation ........................................................................................................ 120 6.3.2 Non-climatic limitation, implications for spread .......................................................... 121

6.4 Avenues for future research ....................................................................................................... 123 6.4.1 Study species – some important unknowns .................................................................. 123 6.4.2 Limitations, and lessons learned ................................................................................... 124

6.5 Conclusions ................................................................................................................................ 125

Appendix A – Supporting information for Chapter 2 .................................................................... 126

A.1 An example MaxEnt model ....................................................................................................... 126

A.2 Supporting data for study species .............................................................................................. 127

Appendix B – Supporting information for Chapter 3 ..................................................................... 137

Appendix C - Supporting information for Chapter 4 ..................................................................... 147

C.1 Road survey methodology ......................................................................................................... 147

C.2 Supporting data .......................................................................................................................... 148

Appendix D - Supporting information for Chapter 5 ..................................................................... 155

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Appendix E - Herbicide trial results ................................................................................................. 165

E.1 Rationale .................................................................................................................................... 165

E.2 Methods ..................................................................................................................................... 165

E.3 Results ........................................................................................................................................ 166

E.4 Summary .................................................................................................................................... 168

Supplementary materials ................................................................................................................... 169

S.1 - IPM coefficients .......................................................................................................................... 169

S.2 - R code for IPMs, adapted from Merow, Dahlgren, et al. (2014) ................................................. 170

References ........................................................................................................................................... 172

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List of tables

Table 1.1 Broad categories of SDMs, with examples and brief description, advantages and

disadvantages of each category, and suitable uses. ............................................................. 4 Table 1.2 Key traits of study species Aeonium arboreum, A. haworthii and Cotyledon orbiculata.

Data on introduced ranges taken from occurrence records (source list Table A.1).

Other traits collated from Webb et al. (1988), additional sources cited in table. ................ 9 Table 2.1 Niche equivalency and similarity of target species between global and New Zealand

ranges, following the methods of Broennimann et al. (2012). Similarity indicates

whether niches in the target ranges are more similar to each other than random

simulations. Asterisks denote bootstrapped levels of statistical significance of D (p ≤

0.05), where they signify rejection of niche equivalency at the 95% confidence level. .... 25 Table 2.2 Sensitivity (Sens.) and projected suitable area (PSA) of global (excluding New Zealand)

and total (global plus New Zealand) BIOCLIM models of Aeonium arboreum,

A. haworthii and Cotyledon orbiculata, tested against the world and New Zealand.

Statistical significance of sensitivity, given projected suitable area, calculated using

Fisher’s one-tailed binomial statistic (* p<0.05, ** p<0.01). Global models

independently validated against New Zealand, total models cross-validated 5-fold

(mean value given). ........................................................................................................... 27 Table 2.3 Projected suitable area (PSA) for Aeonium arboreum, A. haworthii and Cotyledon

orbiculata, with and without constraint by habitat. Sensitivity of constrained models

shown with significance calculated using Fisher’s one-tailed binomial statistic (**

p < 0.01). Percent reduction in projected suitable area, after habitat masks were

applied, is given relative to climate-only models. ............................................................. 29 Table 3.1 Target species traits. Maximum size and time to maximum size from Vogan (2003) and

Royal Horticultural Society (2014). Elevation, precipitation and annual mean

temperature in native, New Zealand, and all other introduced ranges taken from

occurrence data (Table A.1) and Worldclim Bioclim variables [(Hijmans et al. 2005),

available at http://www.worldclim.org]. Minimum elevation for all species in all

regions is 0 MASL. ............................................................................................................ 44 Table 3.2 Number of sites on Banks Peninsula used for cuttings only, seed trays only, or both, in

each bioclimate zone as defined by Wilson (1993). .......................................................... 44 Table 3.3 Modelled seedling establishment (SEst), relative growth (RG) and summer and winter

mortality (SM and WM), at various elevations (MASL), for Aeonium arboreum,

A. haworthii and Cotyledon orbiculata. No random effects included except for SEst

max, predicted seed establishment at the most favourable site using the highest

random site effect. Predictions given for the 95th percentile of the observed distribution

(+), the maximum observed elevation (*, bold), and up to 300 MASL above the

observed limit. The 95% prediction intervals are denoted by ±. Frost and GDD

assumed to increase linearly with elevation, other variables set to constant values. ......... 60 Table 4.1 Total numbers of Aeonium arboreum, A. haworthii and Cotyledon orbiculata flowering

in 2011 (Y1) or 2012 (Y2) only, or both years. Mortality shown as % of all

individuals, broken down into number of plants confirmed dead vs. not re-located.

Number of samples for each models also provided. .......................................................... 77 Table 4.2 Analysis of variance (ANOVA) source tables, showing differences in fecundity among

years (if applicable), sites, and plants (if applicable) for Aeonium arboreum,

A. haworthii and Cotyledon orbiculata. ANOVAs run for numbers of log-standardised

Inflorescences|Plant, Flowers|Inflorescence, and Seeds|Pod. For total numbers

flowering, columns show degrees of freedom, deviance, and residual degrees of

freedom and deviance from a Chi-squared ANOVA of a binomial GLM with year and

site effects. Significant results highlighted in bold and level denoted by asterisks (*),

where; * p < 0.05, ** p < 0.01, *** p < 0.001. .................................................................. 77 Table 4.3 Source tables for one-way ANOVAs on among-site differences in log-standardized

canopy volume and internode length, for Aeonium arboreum, A. haworthii and

Cotyledon orbiculata. Analyses were run on second year data, both across all plants,

and flowering plants only. ................................................................................................. 83

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Table 4.4 Predicted mean inflorescences per plant, flowers per inflorescence and seeds per pods for

Aeonium arboreum, A. haworthii and Cotyledon orbiculata, with 95% bootstrapped

confidence intervals in brackets. Models use mean plant volume or internode length of

all flowering plants, aspect set to east (A. arboreum) or none (C. orbiculata). Seeds

per plant is the product of the three models. ...................................................................... 84 Table 4.5 Parameter elasticity values for GLMMs of inflorescences per plant, flowers per

inflorescence and seeds per pod, calculated against predicted seeds per plant for

Aeonium arboreum and Cotyledon orbiculata. Highest elasticity value per species is

highlighted in bold. ............................................................................................................ 84 Table 5.1 Linear regressions of vital rates of Aeonium arboreum (AA), A. haworthii (AH) and

Cotyledon orbiculata (CO), as used in IPMs. Parameters of each regression shown,

and whether the regression was fitted to experimental (Chapter 3) or survey (Chapter

4) data. Model coefficients are available in Table S.1. Units are plant volume (L),

elevation (MASL), precipitation (mm/year) Frost days, GDD and precipitation were 2-

year annual means for each variable. ................................................................................. 98 Table 5.2 Verification of integral projection models of Aeonium arboreum, A. haworthii and

Cotyledon orbiculata, run at 83 point locations on Banks Peninsula. Sites divided

according to species’ current presence or absence. Sites with predicted population

growth (λ) >1 were classified as suitable, <1 were classified unsuitable. ....................... 103 Table 5.3 Elasticity values of IPM parameters. Perturbation analyses conducted for Aeonium

arboreum, A. haworthii and Cotyledon orbiculata at favourable sites (upper 95th

percentile of λ) and unfavourable sites (lower 95th percentile of λ), with the three

highest elasticities highlighted for each species. ............................................................. 104 Table 5.4 Single factor ANOVA comparing BIOCLIM scores at fundamental presence and absence

locations for Aeonium arboreum, A. haworthii and Cotyledon orbiculata. Fundamental

presences and absences distinguished by the threshold of λ = 1 for IPM predictions. .... 106 Table 5.5 Sensitivity, specificity, under prediction rate (UPR) and over prediction rate (OPR), and

projected suitable area (PSA, %), for Aeonium arboreum, A. haworthii and Cotyledon

orbiculata. All metrics calculated for Banks Peninsula only. Original models

(unrefined BIOCLIM projections) validated against IPM predictions. The same

metrics are shown for refined BIOCLIM projections, calculated against IPM

predictions and true presences. ........................................................................................ 110

Table A.1 Sources and number of occurrence records collected for Aeonium arboreum,

A. haworthii and Cotyledon orbiculata, before data cleaning and resampling. ............... 127 Table A.2 Regions and Köppen-Geiger (KG) classes sampled within for Aeonium arboreum,

A. haworthii and Cotyledon orbiculata niche analyses, and number of samples taken. .. 128 Table A.3 Description of land cover classes (Ministry for the Environment & Landcare Research

2014) that spatially intersect Cotyledon orbiculata occurrence records in New

Zealand. Class descriptions summarized from Thompson et al. (2003). ......................... 135

Table B.1 Source list for Banks Peninsula distribution data of Aeonium arboreum, A. haworthii and

Cotyledon orbiculata. ...................................................................................................... 138 Table B.2 Details of all numbered sites in Figure 3.1. “Use” distinguishes between weather stations

used for precipitation data (P), and field sites used for cuttings only (C), seeds only

(S), or both (CS). Longitude and latitude in decimal degrees (WGS 84), elevation in

MASL. Aspect (cardinal direction) and % overhead canopy cover (CC) measured at

field sites only. Asterisks (*) denote sites where CC is caused by trees (as opposed to

low garden features at seed sites). “Precip.WS” indicates the weather station used for

precipitation data at each field site. ................................................................................. 139 Table B.3 Individual seed weight of Aeonium arboreum, A. haworthii and Cotyledon orbiculata,

and weight of seed and chaff estimated to contain 100 seeds, according to seed source

site. Also given are results of tetrazolium tests, as percentages of seeds found to be

fully stained (viable, high vigour) and pale stained (viable, low vigour). ....................... 141

xi

Table C.1 Details of Aeonium arboreum, A. haworthii and Cotyledon orbiculata survey sites.

Longitude and latitude given in decimal degrees (WGS 1984), elevation in MASL,

aspect to the nearest cardinal point. Habitat and earthquake (EQ) damage are visual

assessments, geological units from G.N.S. Science (2014). Categories of EQ damage

are none, rock fall (RF) or landslides (LS), divided into small (S), moderate (M) and

large (L). .......................................................................................................................... 151 Table C.2 Life stage categories used in surveys of Aeonium arboreum, A. haworthii and Cotyledon

orbiculata on Banks Peninsula. ....................................................................................... 152

Table D.1 List of all point locations for which IPMs were run. Type denotes whether site is a

weather station (WS; data available at http://cliflo.niwa.co.nz/), or a field experiment

(FE) or survey site (FS; see Chapter 3 and Chapter 4). Longitude and latitude in

decimal degrees (WGS 1984), elevation in MASL. Precip.WS denotes the ID of the

weather station used for precipitation values for each site, also available through

CliFlo, * denotes weather stations used for precipitation data only not listed in table,

full names given below table. Species present indicates which species (Aeonium

arboreum, A. haworthii, Cotyledon orbiculata) are present within the same 30-arc-

second grid cell as the site. .............................................................................................. 155 Table D.2 Paired t-test results for mean annual frost days, GDD5 and GDD10 at weather stations

used as IPM locations. Results given for 2-year versus 5-year, 10-year and 20-year

means, with degrees of freedom (DF), t and p-values. Significant results indicated in

bold. ................................................................................................................................. 157 Table D.3 Minimum, mean and maximum correlations (r) between data logger sites and the nearest

weather station over 2011-2012. Minimum and maximum temperature rescaled as

residuals of the site sample mean before calculating correlation coefficient. ................. 158

Table E.1 Scale used for visual assessment of damage to Aeonium arboreum, A. haworthii and

Cotyledon orbiculata six weeks after herbicide treatment. ............................................. 165

Table S.1 Coefficients used in IPMs of Aeonium arboreum, A. haworthii and Cotyledon orbiculata.169

xii

List of figures

Figure 1.1 Photographs of study species a) Aeonium arboreum, b) A. haworthii and c) Cotyledon

orbiculata, showing individual plants (left) and naturalized populations (right). All

photographs taken on Banks Peninsula, Canterbury, New Zealand. ................................. 11 Figure 2.1 Known global distributions of a) Aeonium arboreum, b) A. haworthii and c) Cotyledon

orbiculata, after resampling onto a 30 arc-second grid. Number of presence points per

region labelled. Red points were used for model training; black points removed as

suspected to be plants in cultivation. ................................................................................. 18 Figure 2.2 a-c) Kernel-smoothed PCA biplots of climatic niches, in the global range (red) and New

Zealand range (blue), for a) Aeonium arboreum, b) A. haworthii and c) Cotyledon

orbiculata. Plots generated using 5 bioclimatic variables [(Hijmans et al. 2005),

available at http://www.worldclim.org]. Solid lines delimit total background climate,

dashed lines delimit 50% of background climate. Shading indicates density of

occurrences after kernel smoother applied. Correlation circles show correlation

between bioclimatic variables (see legend, g), with principal component axes for d)

A. arboreum, e) A. haworthii and f) C. orbiculata. ........................................................... 26 Figure 2.3 BIOCLIM global projections of climate suitability, using all available data, for a)

Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata. Model scores

between 1 and 0 signify the position within the n-dimensional climate space. Scores

approaching 1 indicate similarity to the species’ 50th percentile of the species’

rectilinear climate envelope (“core” climate), while 0 signifies that the climate is

outside the 5th or 95

th percentiles of the envelope. ............................................................. 28

Figure 2.4 a) New Zealand projections of final BIOCLIM climate-only models for Aeonium

arboreum, with points showing occurrence records. Model (a) was then constrained by

(b), the mask of habitat suitability to give (c), the final projection of overall suitability.

BIOCLIM scores are percentiles of the species’ distributions in climate space. Scores





Figure 2.5 a) New Zealand projections of final BIOCLIM climate-only models for Aeonium

haworthii, with points showing occurrence records. Model (a) was then constrained by

(b), the mask of habitat suitability to give (c), the final projection of overall suitability.

BIOCLIM scores are percentiles of the species’ distributions in climate space. Scores





Figure 2.6 a) New Zealand projections of final BIOCLIM climate-only models for Cotyledon

orbiculata, with points showing occurrence records. Model (a) was then constrained

by (b), the mask of habitat suitability to give (c), the final projection of overall

suitability. BIOCLIM scores are percentiles of the species’ distributions in climate

space. Scores approaching 1 indicate similarity to the species’ 50th percentile of the

species’ rectilinear climate envelope (“core” climate), while 0 signifies that the

climate is outside the 5th or 95

th percentiles of the envelope. ............................................ 32

Figure 3.1 a) Field sites, and weather stations providing precipitation data, b) field site elevations,

and c) location of Banks Peninsula. Field sites contained cuttings only, seeds only or

both (see legend), site numbers correspond to Table B.2 (site details). Base map is

total annual precipitation with shaded relief, where grey indicates no data.

Precipitation was interpolated from the 30 arc-second Worldclim layer [(Hijmans et

al. 2005), available at http://www.worldclim.org]. ........................................................... 45 Figure 3.2 Mean seedling count at measurement intervals with 95% confidence intervals, for

a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata. Sites are divided

into low (0 – 150 MASL), medium (150 – 400 MASL), and high (400 – 700 MASL)

elevations. Seedling models are based on November 2012 counts. .................................. 52 Figure 3.3 Coefficients of GLMMs of probability of probability of seedling establishment (P[SEst])

± 95% confidence intervals, with fixed (solid) and random (hollow) effects, for a)

xiii

Aeonium arboreum c) A. haworthii and e) Cotyledon orbiculata, and GLMM

predictions (lines) and raw data (points) for b) A. arboreum, d) A. haworthii and f)

C. orbiculata. Predictions use fixed only effects between 0 – 1000 MASL (b, d), and

400 – 1400 mm p.a. (f). For A. arboreum (b), constant precipitation of 733 mm p.a.,

and linear relationships of GDD5 and frost days to elevation are assumed (section

3.3.9). Thus, lines are not fitted to points. ......................................................................... 53

Figure 3.4 Mean relative growth, as lnVolumet+1-lnVolumet, since November 2010 baseline

volumes at low, medium, and high elevations for a) Aeonium arboreum, b)

A. haworthii, and c) Cotyledon orbiculata. Here, t is measured in units of half-years.

Shaded area shows 95% confidence interval of the mean. ................................................ 54 Figure 3.5 GLMM coefficients ± 95% confidence intervals of annual relative growth (RG) models,

calculated as lnVolumet+1-lnVolumet, with fixed (solid) and random (hollow) effects,

for a) Aeonium arboreum, c) A. haworthii and e) Cotyledon orbiculata. GLMM

predictions (lines) and site means with standard errors (points) in years one and two,

shown for b) A. arboreum, d) A. haworthii and f) C. orbiculata. Predictions generated

using only fixed effects between 0 – 1 000 MASL. A linear relationship of annual

frost days with elevation is assumed (section 3.3.9). Canopy cover (CC) is set to zero

for C. orbiculata. Thus, lines are not fitted to points. ........................................................ 55 Figure 3.6 Coefficients of binomial GLMs of summer mortality with 95% confidence intervals, for

a) Aeonium arboreum, c) A. haworthii and e) Cotyledon orbiculata, and percentage of

surviving individuals at each measurement period, at low, medium, and high

elevations for b) A. arboreum, d) A. haworthii and e) C. orbiculata. Percentages

measured out of n = 50 individuals at low and high elevations, and n = 100 at medium

elevations. .......................................................................................................................... 58 Figure 3.7 Logistic GLMM coefficients of winter mortality ± 95% confidence intervals, with fixed

(solid) and random (hollow) effects, for a) Aeonium arboreum, c) A. haworthii and e)

Cotyledon orbiculata, and modelled probability of death (P[Die], lines) and observed

mortality per site (points) vs. elevation, for b) A. arboreum, d) A. haworthii and

f) C. orbiculata. Predictions (lines) generated for small (0.125 L), medium (1 L), and

large (8 L) plants, using only fixed effects between 0 – 1000 MASL. A linear

relationship of annual frost days with elevation is assumed, derived from recorded

data. Consequently, lines are not fitted to points. .............................................................. 59 Figure 4.1 Populations of a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata in

Banks Peninsula and New Zealand (inset), and locations of survey sites (green points,

general region labelled). Background layer shows annual precipitation, interpolated

from Worldclim data, with shaded relief [(Hijmans et al. 2005), available at

http://www.worldclim.org/bioclim]. .................................................................................. 71 Figure 4.2 Coefficients and predictions of P[Flower] GLMMs for Aeonium arboreum (a, b),

A. haworthii (c, d) and Cotyledon orbiculata (e, f). Fixed effect coefficients shown

with 95% confidence intervals (solid points), random effects with maximum and

minimum values (hollow points). Plots b, d and f show modelled probability of

flowering vs. canopy volume (lines). Axis rescaled to ∛(Volume×103), ≈ plant height,

for aesthetics. Proportion of plants flowering at midpoints of volume bins shown

(points) with number of plants in bin (numbers). .............................................................. 78 Figure 4.3 Outputs of Inflorescences|Plant GLMMs for Aeonium arboreum (a, c) and Cotyledon

orbiculata (b, d). Plots a & b show model coefficients, solid points for fixed effects ±

95% confidence intervals, hollow for random effects with maximum and minimum

values. Plots c & d show predicted inflorescences (lines) vs. previous internode length

(mm) and canopy volume (L), for A. arboreum (c) and C. orbiculata (d). Canopy

volume axis rescaled to ∛Volume × 103 (≈ plant height) for aesthetics. ........................... 80

Figure 4.4 Outputs of Flowers|Inflorescence GLMMs for Aeonium arboreum (a, c) and Cotyledon

orbiculata (b, d). Plots a & b show model coefficients, solid points for fixed effects

with 95% confidence intervals, and hollow for random effects with maximum and

minimum values. Plot c shows predicted number of A. arboreum flowers (triangular

points) versus aspect, with observed values in boxplot. Plot d shows predicted number

of C. orbiculata flowers (line) versus canopy volume (L). Axis rescaled to ∛Volume ×

103, ≈ plant height, for aesthetics, observed values shown as points. ................................ 81

xiv

Figure 4.5 Outputs of Seeds|Pod GLMMs for Aeonium arboreum (a, c) and Cotyledon orbiculata

(b, d) and legend for plots c & d (e). Plots a & b show GLMM coefficients, solid

points for fixed effects with 95% confidence intervals, hollow points for random

effects with maximum and minimum values. The reference category for aspect is

north. Plots c & d show predicted number of seeds per pod, versus pods per

inflorescence, in A. arboreum and C. orbiculata respectively. Lines show predictions

for aspect category, points show observed data (see legend). ........................................... 82 Figure 5.1 Graphical representation of confusion matrices validating BIOCLIM against IPM

predictions. Points show BIOCLIM score vs. λ at each location where IPMs were run,

for a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata. Lines indicate

where BIOCLIM > 0 (projected suitable by BIOCLIM) and λ = 1 (threshold for

suitable/unsuitable in IPM). Because BIOCLIM scores all unsuitable sites as 0, lines

are drawn at the lowest BIOCLIM score on Banks Peninsula......................................... 106 Figure 5.2a) New Zealand and b) Banks Peninsula BIOCLIM projections for Aeonium arboreum.

Grey cells are projected as unsuitable by BIOCLIM. Predicted λ (IPM) for each

species shown as graduated red points at each IPM location, black points represent

λ < 1 (unsuitable). Shaded relief shown on Banks Peninsula. ......................................... 107 Figure 5.3a) New Zealand and b) Banks Peninsula BIOCLIM projections for Aeonium haworthii.



λ < 1 (unsuitable). Shaded relief shown on Banks Peninsula. ......................................... 108 Figure 5.4a) New Zealand and b) Banks Peninsula BIOCLIM projections for Cotyledon orbiculata.



λ < 1 (unsuitable). Shaded relief shown on Banks Peninsula. ......................................... 109 Figure 5.5 Refined BIOCLIM projections for b) Aeonium arboreum, c) A. haworthii and c)

Cotyledon orbiculata on Banks Peninsula, with shaded relief, and extent indicator (a).

Categories are: predicted unsuitable by BIOCLIM (blue, unsuitable), predicted

suitable by BIOCLIM but below IPM-based threshold (yellow, likely unsuitable), and

predicted suitable by BIOCLIM and above the IPM-based threshold (red, likely

suitable). .......................................................................................................................... 111

Figure A.1 Distribution of species Y in relation to a climatic variable X. Response curves (red)

generated by a MaxEnt model with linear and quadratic features only (a), and all

“auto-features” (b). In region 1 (R1), the species is most prevalent and occupies a wide

range of climates, but can tolerate conditions in region 2 (R2) although it is less

prevalent. Values of X between R1 and R2 are assumed to be climatically suitable. In

a), suitable habitat in R2 is under-predicted, while in b), climate space between R1 and

R2 is under-predicted. ...................................................................................................... 126 Figure A.2 Frequency histograms of the five bioclimatic variables used in niche analysis and

models of target species, at all global occurrence points. Plots shown for i) Aeonium

arboreum; ii) A. haworthii and iii) Cotyledon orbiculata. Variables are: a) BIO10

(Mean temperature of the warmest quarter, °C × 10); b) BIO11 (mean temperature of

the coldest quarter, °C × 10); c) BIO16 (Precipitation of the wettest quarter, mm);

d) BIO17 (Precipitation of the driest quarter, mm); e) BIO19 (Precipitation of the

coldest quarter, mm). ....................................................................................................... 129 Figure A.3 Frequency of land use classification (Nachtergaele & Petri 2008) in grid cells (5 arc-

minutes) containing Cotyledon orbiculata in a) Southern Africa (South Africa,

Lesotho, Swaziland, Namibia, Mozambique, Angola); b) Europe (Corsica, Spain); c)

the U.S.A.; d) Australia and e) New Zealand. Asterisks denote significance of land use

type given its proportional area, according to Fisher’s exact test (• = p < 0.05,

= p < 0.01). .................................................................................................................. 130 Figure A.4 Density of cattle, goats and sheep (heads per km

2) in grid cells (0.05 decimal degrees)

containing Cotyledon orbiculata (grey) versus randomly-selected background points

(white) in a) U.S.A., b) Europe (Corsica, Spain), c) Southern Africa (South Africa,

Lesotho, Swaziland, Namibia, Mozambique, Angola), d) Australia and e) New

xv

Zealand. Maximum density shown where whiskers extend beyond axes. Data courtesy

of GLW (Robinson et al. 2014). ...................................................................................... 131 Figure A.5 Livestock density of cattle, goats and sheep expressed as heads per km

2 in grid cells

(0.05 decimal degrees) containing Aeonium arboreum (grey) versus randomly-selected

background points (white) in a) U.S.A., b) Europe (Spain, Portugal, Balearic Islands,

Malta), c) Macaronesia (Canary Islands, Morocco, Madeira), d) Australia and e) New

Zealand. Maximum values shown where whiskers extend beyond plots. Data courtesy

of GLW (Robinson et al. 2014). ...................................................................................... 132 Figure A.6 Livestock density of cattle, goats and sheep expressed as heads per km

2 in grid cells

(0.05 decimal degrees) containing Aeonium haworthii (grey) versus randomly-selected

background points (white) in a) U.S.A., b) Europe (Spain, France), c) Macaronesia

(Canary Islands), d) Australia and e) New Zealand. Maximum values shown where

whiskers extend beyond plots. Data courtesy of GLW (Robinson et al. 2014). .............. 133 Figure A.7 a) Frequency of Cotyledon orbiculata occurrence records in land cover classes

(Ministry for the Environment & Landcare Research 2014) and b) farm types

(excluding non-farmland) according to Agribase™ (AsureQuality 2006). Black bars

indicate statistical significance (p < 0.01) of C. orbiculata frequency, given total

occurrences and the proportional area of each class in New Zealand, according to a

one-tailed binomial test. ................................................................................................... 134 Figure A.8 Global a) and New Zealand b) projections of BIOCLIM models for Cotyledon

orbiculata, trained on subset of all occurrence data, with 7 points removed from the

most extreme high elevations in Lesotho. BIOCLIM scores are percentiles of the

species’ distributions in climate space. Scores approaching 1 signify similarity to the

species’ 50th percentile in climate space (“core” climate), and 0 signifies that the cell is

outside of the species’ rectilinear hypervolume. ............................................................. 136

Figure B.1 Map of current distributions, cutting collection sites and seed collection sites, for

a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata on Banks

Peninsula. Location of Banks Peninsula relative to New Zealand also shown (d). ......... 137 Figure B.2 Elevation (MASL) versus total annual precipitation (mm) on Banks Peninsula, taken

from 30-arc-second Worldclim layers [(Hijmans et al. 2005), available at

http://www.worldclim.org]. Grey points show values for entire Peninsula, black points

show values at recorded presence locations of a) Aeonium arboreum b) A. haworthii

and c) Cotyledon orbiculata. ........................................................................................... 140 Figure B.3 Cotyledon orbiculata seeds under microscope at 100 × magnification. Seeds have been

stained with TTC and seed coat removed. Top row show pale and partial staining and

are non-viable due to necrosis of vital tissue. Middle row show full staining indicating

viability and high vigour. Bottom row show no staining and are completely non-

viable. .............................................................................................................................. 142 Figure B.4 Scatterplots showing similar relationships between relative growth, calculated as

[ln (Volumet+1) – ln (Volumet)], and annual frost days and elevation, in both years of

field experiment. Year one indicated by black points, year two by red points. Shown

for Aeonium arboreum (a, b) A. haworthii (c, d) and Cotyledon orbiculata (e, f). ......... 143 Figure B.5 Correlations of elevation with five annual climatic variables (a-e) at field transplant

sites, over both years. Seed tray only sites not used due to incomplete year one data.

Only one year of data presented for solar radiation (e) due to negligible differences

between years. Pearson’s correlation coefficient (r) and statistical significance

indicated in figures, by * (p < 0.05), ** (p < 0.01), or *** (p < 0.001). .......................... 144 Figure B.6 Canopy volume (L) at previous measurement interval of a) Aeonium arboreum, b)

A. haworthii and c) Cotyledon orbiculata, grouped by survival. Relationship between

mean canopy volume, cumulative frost days and % deaths per site, of d) A. arboreum,

e) A. haworthii and f) C. orbiculata................................................................................. 145 Figure B.7 Canopy volume required for 50% survival at a given elevation, in years 1 and 2,

according to final models for a) Aeonium arboreum, b) A. haworthii and c) Cotyledon

orbiculata. Predictions generated along a hypothetical gradient where frost increases

linearly with elevation, and shade is set to zero. ............................................................. 146

xvi

Figure C.1 All 30 arc-second cells surveyed for Aeonium arboreum, A. haworthii and Cotyledon

orbiculata on Banks Peninsula, b) extent indicator. ........................................................ 148 Figure C.2 Maps of populations of a) Aeonium arboreum, b) A. haworthii and c) Cotyledon

orbiculata on Banks Peninsula. Inset maps show New Zealand presences of each

species. Points on Banks Peninsula scaled by population size (Abundant = extensive,

constant; Frequent = extensive, scattered; Occasional = few, scattered; Rare = one

individual). Red points indicate accessible populations, black points inaccessible (e.g.

cliffs). Road centrelines shown in dark grey. .................................................................. 149 Figure C.3 Elevation vs. annual precipitation gradient across Banks Peninsula (grey), and at known

populations of a) Aeonium arboreum, b) A haworthii and c) Cotyledon orbiculata

(black), and at sites chosen for surveys (red). Precipitation data taken from 30 arc-

second Worldclim layer [(Hijmans et al. 2005), available at

http://www.worldclim.org/bioclim]. ................................................................................ 150 Figure C.4 Map of weather stations on Banks Peninsula (n = 8, dark blue points) with precipitation

data for 2010 - 2012, the time period of flowering surveys. Survey sites (n = 24)

shown as green points, all points labelled by site or station name, roads indicated by

grey lines. Weather station data available from CliFlo (National Institute of Water and

Atmospheric Research 2014). .......................................................................................... 152 Figure C.5 Histograms of a) annual growing degree days base 5 (GDD5), b) annual precipitation

(mm), and c) annual solar radiation (KWh/M2), at survey sites of all three target

species. Data shown for both years of surveys. Temperature data taken from site data

loggers, precipitation from the nearest weather station, and solar radiation modelled in

ArcMap 10.1. ................................................................................................................... 153 Figure C.6 Mosaic plots (a-c) and boxplots (d-l) of measured reproductive traits at survey sites in

2012. Columns, from left to right: Aeonium arboreum, A. haworthii and Cotyledon

orbiculata. Rows, from top to bottom: proportion of all plants flowering (black) and

not flowering (grey) with thickness of bars scaled to sample size; and on flowering

plants, inflorescences per plant; flowers per inflorescence; seeds per pod. Survey sites

ordered by increasing GDD10, shown for each site (m-o). ............................................. 154

Figure D.1 Annual frost days, GDD10 and GDD5 from 1992-2012, at weather stations used as IPM

locations (see Table D.1 for abbreviations) ..................................................................... 157 Figure D.2 a) Daily minimum and b) daily maximum temperatures, between December 2010 and

November 2011, at sites with data loggers (black) and at weather stations (red). ........... 158 Figure D.3 Structure of a Lefkovitch Matrix Model (size-structured). Lefkovitch matrices are

conceptually similar to IPMs. In this example, there are 5 size classes, 4 of which are

reproductive, and individuals may grow, shrink or stay the same size in each time step.

Graphical representations of the IPM results of these components are given in Figure

D.4, Figure D.5 and Figure D.6 (the reader should note that the matrices are

transposed in the IPM, but the same concepts apply). ..................................................... 159 Figure D.4 Growth matrices (left) and fecundity matrices (right) at climatically good sites (upper

95th percentile of λ) for Aeonium arboreum (OB1; a, b), A. haworthii (LCP; c, d) and

Cotyledon orbiculata (LB; e, f). Unit of plant size is cm (approximately equal to

height). Colours show transition probabilities between size classes (growth matrices)

and individual fecundity (fecundity matrices). ................................................................ 160 Figure D.5 Growth matrices (left) and fecundity matrices (right) at climatically poor sites (lower

95th percentile of λ) for Aeonium arboreum (MP5; a, b), A. haworthii (TO8; c, d) and

Cotyledon orbiculata (TO8; e, f). Unit of plant size is cm (approximately equal to

height). Colours show transition probabilities between size classes (growth matrices)

and individual fecundity (fecundity matrices). ................................................................ 161 Figure D.6 Stable size distributions (left) and probability of survival versus plant size (right) for

IPMs of Aeonium arboreum (a, b), A. haworthii (c, d) and Cotyledon orbiculata (e, f),

at climatically “good” and “poor” sites (upper and lower 95th percentiles of λ). Site ID

indicated in legend, size classes based on plant height (cm). .......................................... 162

xvii

Figure D.7 Elasticity plots of IPM matrices at climatically good sites (left, upper 95th percentile of

λ) and poor sites (right, lower 95th percentile of λ) for Aeonium arboreum (a, b),

A. haworthii (c, d) and Cotyledon orbiculata (e, f). Plant size units are cm (height). ..... 163 Figure D.8 Bootstrapped distributions (n=1000) of mean BIOCLIM scores at IPM locations where

λ >1 (climate suitable) and <1 (climate unsuitable), for a) Aeonium arboreum,

b) A. haworthii and c) Cotyledon orbiculata. .................................................................. 164 Figure D.9 True skill statistic (TSS), under prediction rate (UPR), sensitivity and specificity of

BIOCLIM projections assessed against IPM predictions and true presences, after

iterative raising of suitability threshold, for a) Aeonium arboreum, b) A. haworthii and

Cotyledon orbiculata. ...................................................................................................... 164

Figure E.1 Damage to Aeonium arboreum plants (0 = no damage, 5 = complete mortality, see Table

E.1) after spraying with Escort (E), Escort with Silmaxx (ES), Grazon (G), Grazon

with Silmaxx (GS), Roundup (R), and Roundup with Pulse (RP)................................... 166 Figure E.2 Damage to Aeonium haworthii plants (0 = no damage, 5 = complete mortality, see Table

E.1) after spraying with Escort (E), Escort with Silmaxx (ES), Grazon (G), Grazon

with Silmaxx (GS), Roundup (R), and Roundup with Pulse (RP)................................... 166 Figure E.3 Damage to Cotyledon orbiculata plants (0 = no damage, 5 = complete mortality, see

Table E.1) after spraying with Escort (E), Escort with Silmaxx (ES), Grazon (G),

Grazon with Silmaxx (GS), Roundup (R), and Roundup with Pulse (RP). ..................... 166 Figure E.4 Examples of before and six weeks after herbicide treatment at selected field sites.

Commercial name of herbicide given in table, site names correspond to Table B.2. ...... 168

1

Chapter 1 - Introduction

1.1 Spatial ecology – the where and why of invasions

All species are limited in their distributions to varying degrees. The question of where particular

species occur, and why, has been integral to our understanding of the natural world since at least the

5th Century BCE (Woodward 1987) and underpins the field of spatial ecology. Despite the apparent

simplicity of the underlying question, spatial ecology is a large field of research that has seen rapid

development with the advent of powerful computers. Substantial research goes into projecting species’

current or potential ranges, forecasting how distributions may change in future, and identifying the

fundamental drivers governing species’ limits. These tasks are not trivial, thanks to a multitude of

underlying factors that shape species’ distributions. At the fundamental level, species are limited by

climate, and this is thought to be the most important factor for understanding distributions at the global

scale (Woodward 1987). Plants adapted to tropical rainforests, for example, evolve mechanisms to

maximise leaf runoff that are disadvantageous in drier environments (Givnish 1984), while insect

development is closely related to temperature and varies among species (Briere et al. 1999). Nested

within these broad-scale climatic tolerances, species are further limited by a hierarchy of non-climatic

factors. Abiotic factors including soil type, land use or microclimate shape distributions within

otherwise climatically-suitable regions, as well as dispersal or migration (Brown et al. 1996). At the

local scale biotic interactions can exclude or facilitate species through antagonism or mutualism

(Pearson & Dawson 2003; Townsend Peterson & Soberón 2012), though some argue that biotic

interactions can also affect broader-scale distributions (Godsoe & Harmon 2012; Wisz et al. 2013).

Thus, the questions that underpin spatial ecology differ depending on scale. Spatial ecology has

practical uses in many disciplines including conservation [e.g. optimal reserve design (Gitay et al.

1991), or predicting population persistence under climate change (Keith et al. 2008)], paleogeography

[e.g. recreating past species’ distributions (Collevatti et al. 2012)], and is also a key tool for

understanding invasive species.

Species’ distributions are dynamic and colonization of novel environments frequently occur in nature

[for an extreme example, see Le Roux et al. (2014)], but anthropogenic influence fuelled by increasing

global connectivity has moved species beyond their native ranges at unprecedented rates (Hulme

2009). Most species introduced to novel environments do not establish, and of those that do, only a

small subset become invasive pests i.e. spread and become problematic (Richardson et al. 2000).

Despite this, invasive species are now a serious ecological problem worldwide. Spatial ecology has

obvious application in managing and preventing invasions. Such applications may include predicting

spread through a landscape (Merow et al. 2011), or for pre-border assessment of species for import

[e.g. Weed Risk Assessments that quantify risk using species’ traits and distributions (Pheloung et al.

1999)]. Hotspots or risk areas for invasion can be identified for management or to monitor for new

2

incursions (Pitt et al. 2009), and preventative measures explored for potential future pests (Guichard et

al. 2014). The latter is particularly important for agriculture as novel pests and pathogens may have

devastating effects on crop yields (Pimentel et al. 2005). Projections of invasions may derive from

species’ traits (Roberts et al. 2011), expert knowledge (Martin et al. 2012; Smith et al. 2012) or

laboratory and field data (Ross et al. 2008; Takahara et al. 2013), but increasingly, spatial modelling is

the tool of choice.

1.2 Making models of reality

As a side effect of its explosion in popularity, spatial modelling is inundated by semantic confusion.

Identical models can be referred to as ecological or environmental niche models (ENMs), envelope

models, predictive habitat models, and bioclimatic models, all of which imply different ecological

interpretations (McInerny & Etienne 2012; Warren 2012, 2013). I therefore adopt the stance of Elith

and Leathwick (2009), hereafter using the more neutral term of species distribution models (SDMs).

Most SDM efforts aim to map environmental suitability for a target species, or may even simulate

spread over time through a landscape. However, all SDMs are approximations of reality, and there

exist numerous approaches each with distinct strengths and weaknesses (Table 1.1). At the simpler end

of the spectrum are top-down models, which infer species’ limits by fitting responses to any number of

environmental variables e.g. climate, soil or land use, against known occurrence locations (correlative

SDMs). Correlative approaches are well suited for inferring broad-scale distributions, are usually

static, and are particularly useful when knowledge of the species’ physiology is limited (Elith 2013).

However, they make a number of assumptions that cast doubt upon their realism (explained in section

1.2.2). Bottom-up approaches are considerably more complex, building predictions of range limits

using knowledge of underlying physiological traits such as metabolic rates (mechanistic models), or

vital rates such as mortality (population modelling). Bottom-up approaches are potentially highly

realistic and accurate if correctly parameterized, but may suffer from a lack of generality, are more

costly and data-intensive to implement, and are sensitive to errors in parameterization (Buckley et al.

2010). Between the two lie fitted process-based models such as CLIMEX (Sutherst & Maywald 1985),

which have higher ecological realism than correlative approaches, but the user is restricted to inbuilt

environmental variables with coarse grain size. There also exist hybrid models which combine bottom-

up and top-down techniques [e.g. Brown et al. (2008)], and ensemble models of that generate

projections from the consensus of multiple SDMs [e.g. Poulos et al. (2012)]. The suite of SDMs to

choose from can appear overwhelming, and it may be tempting to assume that more complex models

are better. This is not necessarily the case; the method should instead be chosen based on the question

at hand (e.g. modelling species’ actual spread vs. potential distributions) and the underlying data (i.e.

is there sufficient knowledge to build a mechanistic model?).

3

1.2.1 Correlative SDMs

By far the most common methods for modelling distributions are correlative (Dormann et al. 2012),

and hereafter I use SDMs to refer to correlative models unless explicitly stated. Correlative SDMs are

popular thanks to a wealth of user-friendly software and low data requirement, and data that are

required (i.e. occurrence records and maps of environmental variables) are often freely available

(Ahmed et al. 2015). Each SDM differs and some have numerous settings that can be tailored to

different scenarios [e.g. MaxEnt (Phillips et al. 2006)], but the general principle is the same for all.

Grid layers of relevant environmental variables are chosen, and their values extracted where the

species are present (and often where they are not). These data are interpreted by the underlying

algorithm, inferring the species’ environmental tolerances from the environmental conditions at

presence (and absence) points. The resulting function is transformed back onto maps of environmental

layers to give a final projection of relative suitability, which may be thresholded to predict presence or

absence of the species in the landscape of interest.

The first SDMs were developed for conservation and were simple presence-only methods that created

envelopes in environmental space around occurrence records, classifying any environment outside the

occupied environmental space as unsuitable [e.g. BIOCLIM (Nix 1986), DOMAIN (Carpenter et al.

1993)]. Despite being used successfully in a number of studies (Booth et al. 2014), presence-only

methods have now fallen out of favour and been replaced by more complex algorithms, capable of

predicting non-linear responses and incorporating interactions between environmental variables. Most

modern SDMs contrast presences with either known or assumed absences (true vs. pseudo absences)

to parameterize response functions to environmental variables. Algorithms to differentiate suitable

from unsuitable locations range from relatively simple generalized linear models (GLMs), to simple

decision-tree approaches (CART), to machine learning (e.g. MaxEnt, SVM, BRTs) and recently,

Bayesian techniques (Dorazio 2014). A thorough description of all SDM methods is beyond the scope

of this thesis, and a number of studies have contrasted the performance of various algorithms (Elith et

al. 2006; Hernandez et al. 2006; Tsoar et al. 2007; Jeschke & Strayer 2008; Webber et al. 2011).

Generally, statistical approaches i.e. where the parameters are prescribed by the user, tend to be out-

performed by machine learning models. Here, good performance is defined by the ability of the SDM

to differentiate presences from absences. While machine learning approaches have higher

discriminatory power, it is important to recognize that there is no “best” method – instead, certain

SDMs are better suited to different applications (Table 1.1). A modeller should take into account the

amount and quality of input data, the robustness of absence data, and whether the consequences are

worse for under-prediction (e.g. invasions) or over-prediction (e.g. conservation). Most importantly,

the species and underlying ecological questions are paramount.

4

Table 1.1 Broad categories of SDMs, with examples and brief description, advantages and disadvantages of each category, and suitable uses.

Type Occurrence

Data

Algorithms Description Advantages Disadvantages Suited to modelling… Examples

Correlative Presence

only (PO)

BIOCLIM1

DOMAIN2

HABITAT3

ENFA4

Simple envelopes/boxcar

techniques/ habitat matching

around presence locations

Very low data

requirement

User friendly

Less affected by

sampling bias

No variable interactions

Prone to under-fitting

All variables equal

No extrapolation

Static

Broad scale

Environmental

suitability

Unreliable/ no absences

Few variables

(Podger et al.

1990;

Zaniewski et

al. 2002)

Presence

background

(PB)

MaxEnt5

MaxLike6

Machine learning, creates

polynomial functions from

PO data and contrasted with

background, then adjusted to

maximise entropy

Low data requirement

User friendly

High performance

Variables weighted to

reduce collinearity

Prone to over-fitting

Sensitive to settings/ inputs

Unstable when extrapolating

Static

Any scale

Environmental

suitability/distributions

Unknown survey effort

Multiple variables

(Pearson et al.

2006; Rodda

et al. 2011)

Presence

absence

(PA)

Logistic regression

GLM7

GAM8

MARS9

Neural nets (ANN)

Decision trees

CART10

RF11

BRT

SVM

Logistic regression: fit

parametric or non-parametric

functions to PA data. Neural

nets: interconnected neurons

of variables weighted as

model learns from data.

Decision trees: Recursive

binary splits of data into

groups based on variable

responses

Flexible to many

applications

High performance

Variables weighted

Prevalence can be

estimated

Absence data needed

Prone to over-fitting

Less user friendly

Highest data requirement of

correlative SDMs

Sensitive to bias and settings

Static

Any scale

Environmental

suitability or

distributions

Well-surveyed sp.

Multiple variables

(Drake et al.

2006; Elith et

al. 2008)

Semi-

mechanistic

PO, PB, PA,

or none

CLIMEX12

Tolerances to pre-defined

variables set by user.

Converts tolerances to

growth/stress indices,

combined to ecoclimatic

index denoting suitability

Ecological meaning

Stable extrapolation

Absences not required

Potentially dynamic

Lower risk of spurious

results

Knowledge of physiology

advantageous

Not user friendly

Restricted to large grain size

Less choice of variables

Black box

Broad scale

Environmental

suitability or

distributions

Sp. with known traits

Extrapolation

(Lozier &

Mills 2011; de

Villiers et al.

2013)

Mechanistic None Niche Mapper13

Uses thermodynamics to

model body temperature and

behaviour from climate and

physiological data

High ecological

meaning

Dynamic

Most stable when

extrapolating

Prevalence estimated

High data requirement

Compounding of error

possible

Time-consuming

Highly sensitive to inputs

Not user friendly

Fine scale

Well-studied sp.

Known physiology

Few explanatory

variables

(Fort et al.

2010; Kearney

2012)

1 (Nix 1986); 2 (Carpenter et al. 1993); 3 (Walker & Cocks 1991); 4 (Hirzel et al. 2002); 5 (Elith & Graham 2009); 6 (Royle et al. 2012)7 (McCullagh & Nelder

1989); 8 (Hastie & Tibshirani 1990); 9 (Friedman 1991); 10 (Breiman et al. 1984); 11 (Breiman 2001); 12 (Sutherst & Maywald 1985); 13 (Kearney & Porter 2009)

5

1.2.2 When SDMs go awry

Despite the popularity of SDMs, they have been criticised for relying on questionable assumptions and

debate continues as to how useful their projections are (Pearson & Dawson 2003; Hampe 2004;

Pearson & Dawson 2004; Sinclair et al. 2010). One common assumption is that the species’ niche

(i.e. the environmental conditions that the species is capable of occupying) is stable across both space

and time. If niche shifts occur, e.g. release from natural enemies after invasion allows occupation of

novel climatic conditions otherwise inaccessible to the species (Keane & Crawley 2002), SDMs may

under-predict suitable conditions. Methods exist to test for niche stability (Broennimann et al. 2012;

Guisan et al. 2014) and it is recommended that niche analyses be carried out prior to modelling. A

second, similar assumption is that the species is at equilibrium (i.e. its distribution is representative of

the entire range of its environmental tolerances), and that occurrence records convey the range of the

species’ tolerances. While complete equilibrium never exists in nature, this becomes problematic for

SDMs when non-equilibrium is severe, as often occurs during invasions (Elith et al. 2010). Non-

equilibrium can be exacerbated by biotic interactions such as competition, and unless these correlate

with environmental variables the model may make erroneous predictions (Hampe 2004; Godsoe &

Harmon 2012). Many SDMs also assume that all environmental variables used are limiting and

relevant to the species. The majority of SDM studies use climate variables based on temperature and

precipitation, such as the Worldclim layers [(Hijmans et al. 2005), available at

http://www.worldclim.org], and while these may not be physiologically limiting (e.g. average annual

precipitation does not directly drive photosynthesis), they are assumed to correlate with limiting

variables (e.g. evapotranspiration). Furthermore, while some SDM algorithms weight variables by

explanatory power, ideally minimizing the effect of redundant variables, it remains vitally important to

remove highly correlated variables and select only those which are relevant to the species (Jiménez-

Valverde et al. 2011). When ecological meaning is disregarded in modelling decisions, spurious

predictions can appear otherwise convincing (Lozier et al. 2009). Because of these pitfalls, the

difficulty in modelling species’ distributions lies not in the running of the SDM but in providing sound

reasoning for modelling choices. Sadly, SDM methodologies are sometimes poorly explained and as a

result it is difficult to evaluate the reliability of projections, as well as SDMs in general.

1.2.3 Complementing SDMs with real-world data

Even using best practice, SDMs are difficult to validate, further obscuring our understanding of their

realism. Usually, SDMs are validated against a subset of presences and (pseudo-) absences held back

from model training, using cross-validation or bootstrapping techniques. However, without sub-setting

data carefully to avoid spatial auto-correlation between training and test data, these practices inflate

estimates of model accuracy (Araújo et al. 2005). Independent validation against data in a distinct

geographic region to training data is considered the gold standard, but it is rarely implemented as

independent data are rarely available and costly to produce [though some notable exceptions are

http://www.worldclim.org/

6

described by Araújo et al. (2005)]. But, even independent validation does not provide definitive

answers when attempting to model the hypothetical e.g. species’ potential distributions. Testing SDMs

of potential distributions against current occurrences penalizes models that predict spread to

unoccupied sites, even if the SDM is correct. Models could therefore be better assessed by comparing

projections with real-world performance data, within and outside of the projected suitable range.

Despite calls for experimental validation of SDM predictions, it is rare in practice due to the high

associated cost and effort [but see Ebeling et al. (2008); Elith et al. (2010); Sheppard et al. (2014)].

Though the cost of testing SDMs against real-world data is undeniably high, it is encouraged because

it provides information that cannot be gathered from either technique alone (Kearney & Porter 2009;

Dormann et al. 2012). Species’ performance data, e.g. plant growth along climatic gradients, can

provide detailed and ecologically meaningful information on limiting variables and thresholds to

establishment. However, such information is usually not spatially explicit and may be difficult to

apply across a landscape. On the other hand, SDMs provide spatially explicit predictions but

translating outputs into estimates of species’ performance, or probability of establishment, is difficult.

By combining SDMs with real-world data, model realism and accuracy can be improved, providing

more practical projections for management and better understanding of the target species (Franklin

2010). More generally, such methods may highlight sources of error in SDMs, how much we should

trust in their projections, and where models can be improved to increase realism and accuracy.

Methods for combining real-world data and SDMs vary and are discussed in detail in later chapters.

Most commonly, they include either testing SDM projected suitability performance [e.g. Ebeling et al.

(2008); Sheppard et al. (2014)] or creating a hybrid model to create more detailed and dynamic

predictions, but under the assumption that the underlying SDM is correct [e.g. Brown et al. (2008);

Franklin et al. (2014)].

1.2.4 Structure of thesis

The purpose of this thesis was to combine correlative SDM approaches with field survey and

experimental data in order to test and improve model projections. This was carried out in the context

of a case study, modelling climatic suitability in New Zealand for three selected non-native plant

species. The themes of this thesis can therefore be divided into two categories – firstly using field data

to complement SDMs, and secondly to quantify climatic limitation and predict the potential

distributions of the study species in their invaded range. The applied aspect of the thesis is described in

subsequent sections. The question of whether SDM projections are validated by real-world plant

performance, and how these two approaches can be combined to improve forecasts, is addressed in

three steps over four chapters. I develop simple climate-only SDMs for the target species, and test

whether the climatic niches are conserved between New Zealand and the global distributions. The two

subsequent chapters analyse field plant performance data, which is integrated into a climate-driven

population model in the final data chapter. Using a novel approach, I validate SDM projections of

climate suitability against predicted population growth. Probable sources of prediction error are

7

discussed, and model projections refined to improve agreement with the population model. This thesis

is one of few studies to experimentally test SDM outputs, and demonstrates the importance of going

beyond conventional validation techniques when predicting in novel climates.

1.3 Alien Crassulaceae of New Zealand

As a study system, I use introduced naturalized Crassulaceae plants in New Zealand. The Crassulaceae

is a large family containing 33 genera (T'Hart 1997) with a cosmopolitan distribution and notable

centres of diversity in Mexico, South Africa, the Mediterranean and Himalayas (van Ham 1995).

Predominantly adapted to arid habitats, Crassulaceae plants have succulent, waxy leaves and often

display xerophytic morphology (e.g. rosulate, mounding or matted forms). All species in the family

are obligate or facultative Crassulaceaen Acid Metabolism (CAM) plants, with two possible

exceptions (Pilon-Smits et al. 1996). In the CAM cycle, evapotranspiration is minimized by the

stomata remaining closed during the day. An adaptation to environmental stress, CAM is most

commonly associated with water limitation but light, temperature, salinity and nutrients also modulate

CAM, and available CO2 is considered the central limiting factor (Luttge 2004). Generally, CAM

facilitates survival in extreme environments at the expense of lower efficiency than C4 photosynthesis

(Black 1973). It is unsurprising then, that the key centres of diversity of the Crassulaceae are

extremely arid. It is precisely because they are generally adapted to hot, dry environments that this

family was chosen as a study system; it was anticipated that climatic limitation might be apparent

under the cooler and wetter conditions in New Zealand. Although some Crassulaceae have traditional

medicinal uses (Ming et al. 2005; Ojewole 2005), they are usually planted for ornamental purposes.

Exotic Crassulaceae were introduced to New Zealand by early European settlers, and were popular

with rock garden enthusiasts (Anon 1871, 1920, 1950). The earliest mention of exotic Crassulaceae

species in New Zealand is a newspaper article describing a herbal remedy using fresh Cotyledon

orbiculata leaves (Anon 1866). Discounting hybrids, 22 non-native Crassulaceae species are now

considered naturalized. New Zealand also has 13 native Crassulaceae species (all in the Crassula L.

genus), but unlike the xerophytic introduced Crassulaceae, most natives are adapted to riparian, saline,

or submerged habitats (Webb et al. 1988).

1.3.1 Selecting three study species

Three Crassulaceae species were selected for study based on their traits and the extent of

naturalization in the region of interest. I eliminated species that, according to Webb et al. (1988) only

exhibit vegetative spread in New Zealand (i.e. mature seed not seen; all three Crassula species,

Echeveria secunda Booth ex Lindl., Sedum decumbens R. T. Clausen and Sedum praealtum A. DC.). I

also mapped occurrences of all exotic Crassulaceae in the region of interest using herbarium data and

existing survey data (full source list Table B.1). Based on the above factors I identified the three

species which gave most cause for concern: Aeonium arboreum (L.) Webb & Berthel., Aeonium

haworthii (Salm-Dyck) Webb & Berthel., and Cotyledon orbiculata (L.).

8

Aeonium arboreum was first described as naturalized in New Zealand in the 1950’s, recorded in

Dunedin (Allan Herbarium 1954) and Banks Peninsula (Healy 1959), but the genus has been present

in New Zealand since the late 1800’s (Anon 1871). An upright branching perennial subshrub,

A. arboreum originates from Morocco where it occurs primarily on cliffs along the Atlantic coast

(Mohammed Ater, pers. comm. 2011). Other than New Zealand, it is naturalized in Australia, the

Canary Islands, the U.S.A. (California), Madeira and the Mediterranean. In New Zealand it occurs as

far north as Auckland and as far south as Dunedin, but predominantly in dry climates close to

residential areas and coastlines. Like all Aeonium species, its fleshy leaves form terminal rosettes, and

leaf scars along the woody stems (internodes) indicate seasonal growth (Jorgensen & Olesen 2000).

Vegetative growth occurs in winter, and in early spring the plant produces multiple compound

inflorescences. Aeonium arboreum, A. haworthii and C. orbiculata all produce small (< 1 mm) wind-

dispersed seeds called dust diaspores (van Rheede van Oudtshoorn & van Rooyen 1999).

Aeonium haworthii was first recorded as naturalized in Auckland (Allan Herbarium 1977). Like

A. arboreum, it is a woody branching subshrub with terminal rosettes and annual internodes, but has a

mounding habit, smaller thicker leaves and smaller inflorescences. This xeromorphic growth form is

indicative of A. haworthii’s habitat in its native range of Tenerife (Canary Islands), where it occurs on

cliffs at relatively high elevations (Lems 1960). Because it has been introduced in mostly the same

regions as A. arboreum, the two overlap substantially in both their global and New Zealand

distributions (Table 1.2). Growth also occurs in winter, but A. haworthii flowers later in the year than

other Aeonium species, in early to mid-summer (Webb et al. 1988).

The third species, C. orbiculata, was first described as naturalized on Banks Peninsula (Allan

Herbarium 1967). However, there is anecdotal evidence of C. orbiculata spreading from gardens in

the region as early as 1947 (Robin Waghorn, pers. comm. 2010). Cotyledon orbiculata is distinct from

the two Aeonium species both in distribution and biology. Its evolutionary origins are South African

(Mort et al. 2005) and it is widely distributed across the whole of Southern Africa as far north as

Angola. Within South Africa there are five varietals with distinct biogeography and habitat

preferences, and as such the taxonomy is highly disputed [specifically, whether each varietal should be

a separate species (Van Jaarsveld & Koutnik 2004); Ernst Van Jaarsveld, pers. comm. 2014)].

According to herbarium records, only C. o. var. orbiculata (L.) and C. o. var. oblonga (Haw.) DC. are

present in New Zealand. Cotyledon orbiculata has been introduced to the same global regions as both

Aeonium species (albeit with fewer records in the Mediterranean and none in Macaronesia), but in the

USA, Australia and New Zealand it is much more widespread. One likely reason for the wide

distribution of C. orbiculata is that unlike Aeonium species, it is not limited to cliffs, outcrops and bare

ground – it also occurs in sparse vegetation (Webb et al. 1988). It is the only species of the three to be

recognized by the Ministry of Primary Industries (MPI) as an unwanted organism (UO), and

propagation, sale and importation of the species is prohibited without a permit (Ministry for Primary

Industries 2015).

9

Table 1.2 Key traits of study species Aeonium arboreum, A. haworthii and Cotyledon orbiculata. Data on introduced ranges taken from occurrence records (source

list Table A.1). Other traits collated from Webb et al. (1988), additional sources cited in table.

Species Clade

(Mort et

al. 2001)

Native

Range

Other

introduced

ranges

Status in NZ First record

in NZ

Growth

form,

height

Flowering

time NZ

Seed size

(mm)

Pollinators &

reproduction

Habitat

A. arboreum Aeonium Morocco Australia

Balearic Is.

Canary Is.

Madeira

Malta

N.Z.

Portugal

Scilly Is.

Spain

U.S.A.

Naturalized

No restrictions

Wellington -

Newspaper;

horticultural

society notes

(Anon 1871)

Upright

subshrub

20-70 cm

Jul-Oct** c. 0.5 Generalist insects

(Jorgensen &

Olesen 2001)

Wind, selfing

(Alamo et al. 1996)

Veg. spread

Coastal cliffs

Volcanic rock

Low scrub

Sand

Rocks

Loess banks

A. haworthii Aeonium Tenerife Australia

France

N.Z.

Spain

U.S.A.

Naturalized

No restrictions

Wellington -

Newspaper;

horticultural

society notes

(Anon 1871)

Mounding

subshrub

< 60 cm

Oct-Dec

(Feb)**

0.6 – 0.7 Generalist insects

(Jorgensen &

Olesen 2001)

Wind, selfing

(Alamo et al. 1996)

Veg. spread

Coastal cliffs

Steep banks

Rocks

Lava rubble

Low open scrub

Loess banks

C. orbiculata Kalanchoe Southern

Africa*

Australia

Corsica

N.Z.

Spain

U.S.A.

Naturalized,

Unwanted

Organism

Nelson –

Newspaper;

herbal remedy

(Anon 1871)

Upright

subshrub

< 50 cm

Dec-Jun** 0.5 - 0.8 Birds, selfing

(Zietsman 1998)

Veg. spread

Coastal cliffs

Beaches

Steep banks

Rock outcrops

Low scrub

Dry depleted grassland

* Known occurrences: South Africa, Lesotho, Namibia, Swaziland, Mozambique, Angola, Zimbabwe.

** According to Webb et al. (1988). In the study region of Banks Peninsula A. arboreum is said to begin flowering in midwinter, but personal observations (JP)

indicate peak flowering occurs around November-December in the study populations, similarly A. haworthii was observed to flower from January-March, and

C. orbiculata from January-April (peaking in February).

10

Prior knowledge and specific traits of the three study species are described in detail in the following

chapters as they become relevant. However, little research has been carried out regarding the ecology

of any of the three, and save for one Masters’ thesis on C. orbiculata (Nghindinwa 2009), the species

have not been studied in New Zealand. There have been occasional small-scale studies of the species’

cold tolerances and fecundity in their native ranges (Lösch & Kappen 1981; Van Coller & Stock 1994;

Alamo et al. 1996; Zietsman 1998), but it is clear that there is insufficient prior information on any of

the three species to assess their climatic limits in New Zealand.

1.3.2 Banks Peninsula

The majority of this thesis focusses on Banks Peninsula, Canterbury, a coastal volcanic region of

1150 km2 situated south-east of Christchurch. It is bounded by Kaitorete Spit in the west (- 43.856,

172.378 decimal degrees WGS 1984), Mount Pleasant in the North (- 43.555, 172.715), Le Bons Bay

in the East (- 43.742, 173.102) and Waihuakina Bay in the South (- 43.898, 172.947). The region was

selected because it is a hotspot for alien Crassulaceae; 15 of the 22 species in New Zealand are

naturalized there, and the cliffs near Sumner and Lyttelton were among the first locations where many

were described as naturalized (Healy 1959). The successful establishment of the Crassulaceae is likely

due to a relatively warm and dry climate in the northern bays (where most populations are), combined

with ample suitable habitat – specifically, coastal cliffs, rock outcrops, roadside cuttings and sparsely

vegetated slopes (Webb et al. 1988). As the species are ornamental, garden escapes are the most likely

invasion pathway, and although most species appear to have just a few small populations, local experts

have expressed concern over continued spread and some species are unofficially controlled (Di Carter,

Chris Challies, pers. comm., 2010). On Banks Peninsula, dense populations of A. arboreum are visible

on cliffs and roadside cuttings (Figure 1.1a) but are mainly limited to areas surrounding the towns of

Sumner and Diamond Harbour, and it is the least widespread of the three species. Aeonium haworthii

occurs in many of the same locations as A. arboreum but is more widespread, reaching further around

the northern coastal cliffs than its congener. Cotyledon orbiculata is the most widespread of the three

on Banks Peninsula. It has near-continuous populations on the coastal cliffs between the northern and

eastern bays, and there are occasional large populations in grassland (Figure 1.1c).

Invasions are of particular concern on the Peninsula because it is known as Canterbury’s biodiversity

hotspot, boasting a number of locally endemic plants and invertebrates (Wilson 1986). Rock outcrops,

prone to invasion by the non-native Crassulaceae, are refugia for 50% percent of the region’s

endemics (Wiser & Buxton 2009), and the coastal volcanic cliffs have been recently recognized as a

naturally uncommon ecosystem (Holdaway et al. 2012). Despite the concern over future regional

spread of alien Crassulaceae, their current and potential distribution limits are unknown and their

climatic tolerances have been largely unexplored. Banks Peninsula’s steep terrain provides a useful

backdrop for studying the species’ climatic tolerances, as the highest elevations are likely too cold and

wet for these warmth-loving xerophytes. While the northern bays of the Peninsula are ostensibly

suitable, the inland peaks reach some 919 metres above mean sea level (MASL) and average

11

precipitation varies from 600-2000 mm per year (Wiser & Buxton 2009). Banks Peninsula is therefore

a practical and ecologically relevant choice for studying the climatic limitation of the study species in

New Zealand.

a) Aeonium arboreum

b) Aeonium haworthii

c) Cotyledon orbiculata

Figure 1.1 Photographs of study species a) Aeonium arboreum, b) A. haworthii and c) Cotyledon

orbiculata, showing individual plants (left) and naturalized populations (right). All photographs taken

on Banks Peninsula, Canterbury, New Zealand.

12

1.4 Thesis objectives

The specific objectives addressed in this thesis are:

1. Are the current distributions of A. arboreum, A. haworthii and C. orbiculata in New

Zealand climatically distinct from their distributions elsewhere, and what are their

potential distributions as estimated using SDMs? (Chapter 2)

2. Is there evidence that climate limits the distributions of these species on Banks Peninsula,

and how do demographic processes correlate with climate within and beyond the species’

current distributions? (Chapter 3)

3. Is variation in fecundity in naturalized populations on Banks Peninsula related to variation

in local climate? (Chapter 4)

4. How well do SDMs predict the actual performance of the target species on Banks

Peninsula, and can field data be used to improve SDM projections? (Chapter 5)

To answer my first objective, I use SDMs to estimate the potential distributions in New Zealand of the

study species, firstly using climate alone, then constrained by non-climatic factors. I test whether the

species’ distributions in New Zealand are climatically novel compared with their distributions

elsewhere, and explore the implications for ongoing spread. In the remaining chapters I focus on

climatic limitation on Banks Peninsula, firstly using transplant experiments to test how germination,

growth and survival of the species varies along an elevation gradient. The field experiment also

investigates how close the three species are to their climatic limits in the region. In the fourth chapter,

I test whether fecundity (flowering and seed production) varies among naturalized populations in the

region. Finally, I synthesize the information in the previous chapters into a climate-driven population

model, and test climate-only SDMs against predicted performance. I also refine regional projections of

climatic suitability for the species and explore the relative risk each species poses to Banks Peninsula.

To my knowledge, this is the first study of the target species across multiple stages of their life cycles,

and the first to test their climatic limitation in New Zealand.

1.5 Thesis style

The thesis data chapters (Chapters 2-5) are written in the style of self-contained manuscripts, with the

intention of publication at a later date. Each chapter addresses a separate objective, as described above.

I have endeavoured to minimize any resulting repetition. The final chapter discusses the findings as a

whole, with a focus on potential spread of the study species on Banks Peninsula.

13

Chapter 2 – Modelling the global and New Zealand niches of alien

Crassulaceae indicates invasion of novel climates

2.1 Abstract

Correlative species distribution models (SDMs) are increasingly used to identify suitable

environments where non-native species might establish. Typically, SDMs fit response functions to

climatic variables using species’ occurrence data. However, non-climatic factors often prevent

establishment in otherwise suitable climates, thus restricting distributions in geographic and climatic

space. Such discontinuities can lead to spurious model projections that seriously affect estimates of

species’ potential distributions. This chapter presents a case study modelling climatically suitable

habitat for three non-native species naturalized in New Zealand, all of which have distributions that

are strongly influenced by non-climatic factors. The study species, Aeonium arboreum, Aeonium

haworthii and Cotyledon orbiculata, are succulent xerophytes with specific habitat requirements

(predominantly bare rock) and native ranges that differ climatically to New Zealand (Morocco,

Tenerife and South Africa, respectively). To provide national-scale assessments of suitable habitat in

the introduced range, a three-step method is applied. First, climatic novelty is assessed in the New

Zealand occupied ranges versus the global distributions, and discontinuities shown in the species’

occupied climatic niches. Second, informed by the niche analyses climate envelope models are trained

with data from outside of, and then including, New Zealand, to project suitability in the introduced

range. Third, to refine projections of at-risk habitat, model outputs are constrained by non-climatic

factors, using knowledge of the species’ biology and inferential spatial analyses. Results show that

C. orbiculata poses a larger threat to New Zealand than both Aeonium species, and that while models

classify much of the country as climatically suitable, availability of suitable habitat for Aeonium

species is low. New Zealand represents an expansion of the global occupied niche for all three species,

suggesting that further expansion into novel climates cannot be discounted. This is the first study of

the potential distributions of the three species in New Zealand, and demonstrates a method for

modelling distributions of species that are strongly limited by non-climatic factors.

Keywords: Crassulaceae, invasions, New Zealand, niche, SDM, BIOCLIM

2.2 Introduction

Biological invasions are a pressing ecological issue worldwide (Sutherland et al. 2013). A vital

component of prevention and control of invasions is estimating where non-native species may

encounter suitable environmental conditions for establishment, and pest risk modelling is integral to

this process (Venette et al. 2010). Species Distribution Models (SDMs) were originally developed for

use in conservation biology (Booth et al. 2014), although they are now commonly used to estimate

potential distributions of non-native species (Elith & Leathwick 2009) despite problems with

14

extrapolation into novel climates (Sutherst & Bourne 2009; Webber et al. 2012). Although most

commonly used to infer climatic suitability for target species [e.g. Di Febbraro et al. (2013); Peña-

Gómez et al. (2014)], SDMs correlate any number of environmental variables with species’

occurrence data to infer suitable habitat [e.g. Randin et al. (2009); Vicente et al. (2011)]. However,

SDMs rely on a number of assumptions that make their application to invasions problematic.

Two concepts central to SDMs, particularly when modelling invasions, are niche and equilibrium. The

term niche encompasses many concepts (Grinnell 1917; Elton 1927; Hutchinson 1957), but commonly

indicates the conceptual space in n dimensions along axes of limiting environmental variables that a

species may potentially occupy as a result of its biological traits. This is similar to Hutchinson’s

fundamental niche (1957), which is constrained by biotic and other factors resulting in a realized

niche. A species at equilibrium, meanwhile, occupies all suitable areas within the geographic region of

interest, and while species are rarely present in all suitable locations, extreme non-equilibrium

distributions can misrepresent species’ climatic limits (Araújo & Pearson 2005). The niche and

equilibrium of the species being modelled are important, as most SDMs assume that a species’

geographic distribution reflects its niche, that the niche does not change over space or time (niche

stability), and that the species is sufficiently close to equilibrium to infer climatic tolerances (Wiens et

al. 2009). Unfortunately, assumptions of niche stability and equilibrium are often violated during

invasions (Broennimann & Guisan 2008; Elith et al. 2010). During the early stages of invasion, spread

may be ongoing and the species will be far from equilibrium (Sutherst & Bourne 2009; Václavík &

Meentemeyer 2012). Furthermore, although some studies suggest that niche conservatism is the norm

(Petitpierre et al. 2012; Strubbe et al. 2013), niche shifts, for example through release from natural

enemies (Keane & Crawley 2002), have been posited in a number of systems (Broennimann et al.

2007; Gallagher et al. 2010; Langer et al. 2013). It is therefore a vital first step when modelling the

distribution of a species to determine whether niche stability and equilibrium is a reasonable

assumption. If not, model uncertainty is high, as extrapolation into novel climates is inherently risky

(Webber et al. 2011; Mesgaran et al. 2014). If a species’ climatic niche in the invaded range is

otherwise unrepresented by its distribution elsewhere, it is difficult to infer whether continued

expansion into novel climates will occur.

Even in the absence of niche shifts and extreme non-equilibrium, estimating climatic suitability using

SDMs becomes difficult if a species is strongly limited by non-climatic factors (Sutherst et al. 2007).

Factors such as natural enemies, dispersal limitation and land use affect distributional patterns, and are

nested hierarchically within the climate envelope (Brown et al. 1996; Mackey & Lindenmayer 2001).

Such constraints can cause fragmentation (disjunct distributions) over both geographic and climatic

space, sometimes likened to “Swiss cheese” (Brown et al. 1996; Kriticos et al. 2015). Whilst all

species experience some degree of non-climatic limitation (Brown et al. 1995), in extreme cases,

SDMs may be unable to reconcile populations of the same species as having the same climatic

requirements (Godsoe 2010). This is because most correlative SDMs fit climatic response curves to

15

frequency distributions of occurrence data, and these responses may be biased by discontinuities in the

species’ distributions, e.g. those caused by non-climatic limitation. Depending on the types of

functions fitted to the occurrence data, many SDMs will under-predict the range of suitable climates in

such situations (Webber et al. 2011). Under-predicting suitable habitat is undesirable when modelling

invasions, as it under-estimates pest risk (Sutherst 2013). For an illustration of how non-climatic

limitation may cause SDMs to under-predict, see Section A.1 and Figure A.1. Despite the problems of

niche instability, non-equilibrium and disjunct distributions when using SDMs to model invasions,

there are many available methods to minimize the associated biases. These might include sub-

sampling data or correcting for sampling bias (Kramer-Schadt et al. 2013), modelling disjunct

populations separately or comparing models fitted to different combinations of ranges (Wharton &

Kriticos 2004; Fourcade et al. 2014), testing for novel conditions (Elith et al. 2011; Mesgaran et al.

2014), and selection of an appropriate model for the task (Elith & Graham 2009). There is no “one-

size-fits-all” method, but it is clear that failure to investigate or account for a species’ distribution in

climate space can seriously compromise the reliability of model projections.

The goal of this study was to model potentially suitable habitat for three non-native succulent plants

naturalized in New Zealand, informed by their known global distributions and climatic niches, at a

scale suitable to national-scale pest management. All three species are in the Crassulaceae family:

Aeonium arboreum, A. haworthii, and Cotyledon orbiculata. Their establishment in New Zealand is

surprising due to the comparatively hot and dry conditions of the native ranges. They originate from

Morocco, Tenerife and South Africa, respectively, and these origins are reflected in their utilization of

Crassulacean Acid Metabolism (CAM) photosynthesis, commonly an adaptation to arid conditions

(Luttge 2004). They are present in a number of localities in both the North and South Islands of New

Zealand, and localized spread appears to be ongoing, partly facilitated by high output of viable seed

(Webb et al. 1988). This is of concern to biosecurity managers as they form dense populations that

potentially threaten native species, and C. orbiculata is poisonous to a number of animals (Botha &

Penrith 2008).

In addition to hypothesized climatic limitations, non-climatic factors may strongly influence all three

species’ potential distributions in New Zealand. Literature suggests that they predominantly occur on

bare surfaces such as cliffs, roadside cuttings and rock outcrops, exclusively so for both Aeonium

species (Webb et al. 1988; Bramwell & Bramwell 1990). It is also thought that they are shade

intolerant (Vogan 2003), especially C. orbiculata, which produces photoprotective leaf wax (Barker et

al. 1997). Land use may also be important for C. orbiculata, which can occur in sparse vegetation

(Webb et al. 1988; Van Jaarsveld & Koutnik 2004). Strong non-climatic limitation is ecologically

plausible as CAM photosynthesis is an adaptation to multiple environmental stressors, e.g. water

limitation, allowing plants to occupy stressful niches at the cost of lower maximum potential

photosynthetic efficiency. Hence, CAM plants are less competitive than their C3 and C4 counterparts

when environmental resources are relatively abundant (Black 1973; Grime 1979; Luttge 2004). The

16

target species might therefore be restricted to specific habitats by an inability to compete in other

environments, considerably altering their potential distributions in New Zealand. To provide a useful

estimate of environmental suitability for all three species, both climatic and non-climatic factors are

therefore taken into account.

2.2.1 Aims

1. To investigate whether the global realized niches of A. arboreum, A. haworthii and

C. orbiculata are conserved in New Zealand.

2. Based on the species’ climatic niches, to use an appropriate SDM to infer suitable climatic

conditions in New Zealand.

3. Using a priori knowledge of the target species and inferential spatial analysis, to characterize

habitat suitability according to non-climatic factors in New Zealand, and constrain projected

climatic suitability by habitat to estimate overall environmental suitability.

2.3 Methods

2.3.1 Study species

The study species are each native to a distinct region but all are adapted to hot, semi-arid climates;

A. arboreum is native to Morocco, A. haworthii to Tenerife (Canary Islands), and C. orbiculata to

South Africa (Webb et al. 1988). Other areas of documented naturalization for all three species

include California (U.S.A.) and Australia (Fuller & McClintock 1988; Hussey et al. 2007). Climatic

limitation is expected under the comparatively cool and wet conditions of New Zealand, but the full

extents of the species’ tolerances are unknown. While horticultural guides list all three as frost

sensitive (Vogan 2003), studies report freezing avoidance and acclimation to around - 10 °C in

closely-related Aeonium species and C. orbiculata (Lösch & Kappen 1981; Van Coller & Stock 1994).

The ecophysiology of the three species has been occasionally studied in their native ranges (Alamo et

al. 1996; Barker et al. 1997), and there are no studies from their introduced ranges. Their potential

distributions in New Zealand are therefore highly uncertain. All three species are present in both the

North and South Islands, forming locally dense populations along coastlines. Their distributions in

New Zealand appear to be influenced by human activity, as they commonly occur close to cities and

residential areas. This perhaps reflects propagule pressure from gardens (Healy 1959), a common

factor in plant invasions (Groves et al. 2005; Hulme 2007, 2011). There is potential for ongoing

colonization due to the species’ high fecundity (Alamo et al. 1996; Zietsman 1998), facultative

vegetative reproduction and high population density, along with wind dispersal (van Rheede van

Oudtshoorn & van Rooyen 1999). Regional spread is apparent along coastal cliffs and rock outcrops,

leading to concern over the species’ potential impacts in habitats that provide refugia for endemic and

threatened species (Wiser & Buxton 2009). Cotyledon orbiculata is now an unwanted organism under

17

the Biosecurity Act (Ministry for Primary Industries 1993), meaning that sale and propagation of the

plant is prohibited, and it was under official surveillance in Auckland until 2012 (Auckland Regional

Council 2007).

2.3.2 Distribution data

Global species’ occurrence data was collated from online data portals, herbarium records, botanical

journals, vegetation surveys and personal communication with local residents and experts (for full

source list, see Table A.1). Where occurrence locations were unclear, the surrounding area was

searched using Google Street View (https://maps.google.com). This also resulted in 19 additional

presences across the three species where they had previously not been recorded. Harvesting

occurrence data using Google Street View was tested by Rousselet et al. (2013) and found to be

robust. Some varieties of C. orbiculata were excluded from the dataset because they are not currently

present in New Zealand and have distinct biogeographic patterns, namely, C. o. var. flanganii (Schönl.

& Baker f.) Töelken, C. o. var. dactylopsis (L.) Töelken and C. o. var. spuria (L.) Töelken. The

variety C. o. var. dactylopsis occurs at high elevations (Scott & Springfield 2004) and C. o. var. spuria

inhabits depressions in riverbanks (Mort et al. 2005). Records where variety was unknown were

included. From Morocco, nine out of the ten A. arboreum records were obtained through personal

communication with local experts. Canary Island data for A. haworthii were obtained primarily

through a biodiversity survey of habitat types (Ministerio de Agricultura Alimentación y Medio

Ambiente 2005) and a floristic guide to the Canary Islands (Bramwell & Bramwell 1990), which

broadly describes the regions in which A. haworthii is found. The survey data are polygon maps

showing Aeonium dominated habitat, including A. haworthii. Polygons were converted to a 30 arc-

second raster and the centroid of each cell containing Aeonium converted to point locations,

constrained within regions that Bramwell and Bramwell (1990) describe as containing A. haworthii.

The resulting global occurrence datasets were cleaned and resampled, to partly reduce the effects of

biased and auto-correlated data in the calculation of the goodness of fit statistics. Occurrence data

were cleaned by removing records where their associated description and location data indicated that

the plants were likely to be indoor cultivars. The cleaned point location records were then converted to

WGS 1984 latitude/longitude coordinates, then resampled to centroids of 30 arc-second grid cells

containing presences, to match the grain size of environmental layers. The resulting occurrence

datasets contained 198 records for A. arboreum, 171 for A. haworthii and 725 for C. orbiculata

(Figure 2.1). Despite resampling, there is notably a strong bias towards Southern Africa for

C. orbiculata. In New Zealand there is a bias towards the region of Banks Peninsula for all three

species, which contained 52% of all New Zealand Aeonium records, and 75% of all New Zealand

C. orbiculata records. While Banks Peninsula contributes only 9, 12 and 8% of global occurrences of

A. arboreum, A. haworthii and C. orbiculata respectively, the potential bias is an important

consideration in model selection and interpretation of outputs.

18

Figure 2.1 Known global distributions of a) Aeonium arboreum, b) A. haworthii and c) Cotyledon

orbiculata, after resampling onto a 30 arc-second grid. Number of presence points per region labelled.

Red points were used for model training; black points removed as suspected to be plants in cultivation.

19

2.3.3 Environmental variables

Nineteen 30 arc-second bioclimatic variables [(Hijmans et al. 2005), hosted at www.worldclim.org],

were available for niche analyses and SDMs. Because all variables contribute equally in the niche

analyses and the chosen SDM, it was particularly important to choose a subset based on the species’

known requirements and the correlation between variables. Pearson’s correlation coefficient was

calculated for all 19 variables within all countries containing presences, and highly correlated

variables (r > 0.8) were removed. In addition, histograms of the frequency distributions of the 19

variables across all presence locations were compared with histograms across the global background.

Variables that poorly distinguished the occupied range from the global background were discarded

(see Figure A.2 for histograms of the final variables).

Five common climate variables were selected for all three species, since they have similar geographic

distributions and ecophysiology: mean temperature of the warmest quarter (BIO10), mean temperature

of the coldest quarter (BIO11), precipitation of the wettest quarter (BIO16), precipitation of the driest

quarter (BIO17), and precipitation of the coldest quarter (BIO19). The variables BIO10 and BIO11

were chosen as the species are adapted to hot environments and are believed to be frost-sensitive

(Médail & Quézel 1999; Vogan 2003; Royal Horticultural Society 2014). The variable BIO16 was

chosen as desert succulents often depend on seasonal pulses of rainfall (Ogle & Reynolds 2004), and

BIO17 as it is thought that for at least one of the species flowering time aligns with the dry season

(Harris & Reynolds 2004). Furthermore, their inflorescences are large and fleshy (Zietsman 1998), and

personal observations in New Zealand revealed that in wet environments, flowers of C. orbiculata

may rot. Hence, they may require a distinct dry period to facilitate dehiscence. Finally, BIO19 was

included as succulent species are expected to be sensitive to high rainfall under cooler temperatures,

when potential evapotranspiration is lower and plants may become waterlogged. This is especially

likely for C. orbiculata, which commonly experiences hot, dry winds immediately after high rainfall

in the native range (Eller & Ferrari 1997).

2.3.4 Niche analysis

Prior to calibrating an SDM, it is good practice to perform a niche analysis to highlight issues of niche

shifts, non-analog climates and occupancy patterns that may affect model performance. Niche analyses

were used to assess whether New Zealand is climatically novel compared with the species’ global

distributions, following the methodology of Broennimann et al. (2012). This technique plots the two

realized niches of interest in climate space against user-defined background areas, where niches are

smoothed to minimize occurrence density bias. In addition, it calculates the proportion of niche

equivalency, or overlap [D; (Schoener 1970)], and similarity between the niches. Statistical

significance of equivalency is tested by pooling and randomly splitting all occurrences 100 times and

D calculated for each split. If the observed D is outside 95% of simulated values, the niches are

considered significantly non-equivalent. Similarity is measured by randomly sampling within the


20

climate space of one region, and calculating D against the observed niche in the other. This process is

repeated 100 times for each region, and if observed D is greater than 95% of simulated values the

niches are considered more similar than by chance.

Regions of interest were defined as the global range (the world excluding New Zealand) and New

Zealand. The background area should represent the climate where the species could reasonably be able

to colonize, because including climate extremely different to the niche, or not available to the species

because of geographic barriers, can exaggerate niche divergence (Barve et al. 2011). Background area

is often defined using known dispersal distances and barriers to dispersal, but because all three

species’ dispersal abilities are unknown and their propagation is not restricted outside of New Zealand,

it was not practical to use such an approach. Instead, within New Zealand the five bioclimatic

variables were randomly sampled at 10 000 points, no less than 1 km apart within all islands

containing occurrence records for at least one species (the North, South, Stewart and Chatham

Islands), assuming they are likely to have been planted in gardens throughout the country. The global

background was delimited to include only countries in which we had occurrence records. Sampling

was further restricted to within the same Köppen - Geiger classification as each species is found (see

Table A.2) to avoid including extremely different climates to the species’ niches in large countries

e.g. Alaska (USA). Within these regions, up to 50 000 points no less than 10 km apart were randomly

generated for sampling background climate.

2.3.5 Model of climate suitability

Due to the patchy global distributions of the target species and distinct climatic conditions in New

Zealand compared with the native ranges, SDMs that generate climatic response curves based on

occurrence records were likely to under-predict suitable habitat (as illustrated in Figure A.1).

Consequently a simpler SDM was chosen, BIOCLIM (Nix 1986), as it does not derive response curves

and it is largely unaffected by clustering or sampling biases within the occupied climate space.

BIOCLIM was the first SDM to be widely used, and was a popular modelling tool for over 20 years

(Booth et al. 2014). It is a presence-only model, based on Hutchinson’s n-dimensional niche concept

(Hutchinson 1957) and loosely on Shelford’s Law of Tolerance (Shelford 1931). BIOCLIM defines a

rectilinear hypervolume around all known presences with each climatic variable as a distinct

dimension, and the outer limits are defined by the climatic extremes associated with species

occurrence records. Within this hypervolume, it calculates a percentile distribution of occurrences for

each variable, and a BIOCLIM score between 0 and 1 is derived from the distance to the 50th

percentile or median, i.e. the centre of the rectilinear envelope. Low scores indicate greater distance,

and the minimum BIOCLIM score of all variables is used as the final score for each grid cell. Scores

of 1 are rarely observed, as it signifies that all environmental variables are equivalent to the 50th

percentile of the species’ distribution, while the commonly observed zero score indicates that one or

more variables is outside of the 5th - 95

th percentile range (Hijmans et al. 2014).

21

In recent years BIOCLIM has declined in use, overtaken by more complex tools such as MaxEnt

(Phillips et al. 2006). It has been criticized for low specificity and a tendency to over-predict, a

product of the rectilinear definition of the niche (Townsend Peterson 2011). In addition, BIOCLIM

cannot model interaction effects between variables, and a number of studies have reported low AUC

(Fielding & Bell 1997) and Kappa (Cohen 1960) relative to other models (Elith et al. 2006; Drake

2014; Tessarolo et al. 2014). While BIOCLIM is clearly unsuited to many SDM studies, the degree of

model complexity should be grounded in the ecological question and characteristics of the underlying

data (Merow, Smith, et al. 2014). BIOCLIM’s coarse envelope, defined by the species’ extremes, is

better suited to modelling the study species’ potential distributions than complex models with

functions likely to over-fit and under-predict suitable habitat.

Three BIOCLIM models were run for each species in the R package dismo (Hijmans et al. 2014; R

Core Team 2014), using the same five bioclimatic variables as for the niche analyses. BIOCLIM’s

two-tailed settings were chosen (i.e. cells are marked unsuitable where climate variables fall above the

maximum where the species occurs, and below the minimum). The first models were trained on global

data (world occurrence data excluding New Zealand), to determine whether distributions in New

Zealand were predictable based on the global range alone. The second models were trained on five

random subsets of total data (global data plus New Zealand), each comprising 80% of all available

data, setting the remaining 20% aside for cross-validation. The mean predicted value of all five

projections was then calculated. The third, final models were trained on one run with total data, which

were compared with the cross-validated models before being refined by non-climatic constraints.

2.3.6 A priori non-climatic constraints

The study species’ biology suggests that non-climatic factors contribute strongly to environmental

suitability, and non-climatic range limitation was evidenced by the species’ clustered distributions in

geographical and climatic space. Although over-prediction is preferable to under-prediction when

modelling invasions, over-prediction risks unnecessary spending on management of low-risk species

(Guisan et al. 2013). The final New Zealand BIOCLIM projections were therefore constrained by non-

climatic factors to provide more realistic projections of environmental suitability for the target species

than those with climate alone. Two separate masks mapping non-climatic limiting factors, hereafter

referred to as “habitat suitability” masks, were created for New Zealand. One mask was created for the

two Aeonium species and one for C. orbiculata, as the specific non-climatic limitations appear to

differ between the two. Although all three species grow on bare surfaces such as cliffs, outcrops and

roadside cuttings (Webb et al. 1988), Aeonium species are exclusively found in these habitats whereas

C. orbiculata may grow in sparse vegetation such as grasslands (Van Jaarsveld & Koutnik 2004).

Suitable habitat for Aeonium species was defined a priori according to knowledge of the species and

its distribution, taken from floras (Webb et al. 1988; Bramwell & Bramwell 1990), local experts

(Mohammed Ater, pers. comm. 2011) and habitat descriptions associated with herbarium records.

22

Suitable habitat included cliffs (sea and inland), bare rock (including coastal rocks and outcrops),

quarries, embankments and road cuttings, as these are where the species are most commonly

described. In addition, urban and residential areas were included as Aeonium species are grown and

sold as ornamental plants, and are therefore likely sources for naturalization. All aforementioned

features were selected from the NZ Mainland Topo50 topographic shape files (CC-By Land

Information New Zealand, http://creativecommons.org/licenses/by/3.0/nz/), then converted to a 30 arc-

second raster layer with a buffer of 1 km. This allowed for unmapped small cliffs and outcrops, under

the assumption that large rocky habitats are likely to have similar microhabitats in the surroundings,

and gave flexibility to allow for geo-referencing errors in occurrence records.

2.3.7 Land use constraints for C. orbiculata

Land use was hypothesized to be an important additional habitat factor for C. orbiculata, as it is

known to grow in sparse vegetation (Webb et al. 1988), and, in the native range at least, likely co-

occurs with livestock as it regularly causes stock poisonings (Botha & Penrith 2008; Botha 2013). The

importance of land use was tested using a similar method to that used by Kriticos et al. (2015), first

subdividing known presence locations into five major regions: Southern Africa (S. Africa, Lesotho,

Swaziland, Namibia, Angola and Mozambique); Europe (Spain and Corsica); the U.S.A.; Australia;

and New Zealand. Presence points were spatially intersected with the FAO Land Use Systems of the

World (LUS) dataset (Nachtergaele & Petri 2008), with presence data resampled to 5 arc-minutes to

correspond with the layer. The LUS divides land use into 37 categories describing dominant

vegetation (forest, grassland, shrub, etc.), livestock density (low, moderate or high), agricultural

activities and irrigation, in addition to urban areas and water bodies.

Because of the possible association of C. orbiculata with livestock, the importance of grazing

activities was investigated by spatially intersecting occurrence points with density of sheep, goats and

cattle provided by the FAO’s Gridded Livestock of the World v1.0 (Robinson et al. 2014). This

dataset gives projected estimates of heads per km2 based on census data from 2005, at a 3 arc-minute

resolution. Densities at occurrence points were compared with a randomly sampled background of up

to 500 000 points no less than 10 km apart, in each of the five major regions. I also attempted to

investigate whether soil type or underlying geology was important, but due to limited data in some

global regions and the wide range of soil and rock types C. orbiculata is found on, there was no

discernible pattern. These covariates may be better suited to an a priori analysis as used for Aeonium

species, but would require initial knowledge of the species’ preferences.

To minimize the likelihood of geo-referencing error and microhabitat affecting land use constraints for

C. orbiculata, results of the spatial analysis were tested for statistical significance. The one-tailed

binomial statistic (Webber et al. 2011) was calculated for land use classes in each of the five regions.

The statistic estimates the probability of the observed patterns arising by chance using the proportion

of occurrences in the region falling within a given land use class, and the proportional area between

23

0 and 1 of each land use class in the region. Because of the high number of occurrences and large

areas involved, a threshold p-value of 0.01 was chosen for significance.

The analyses revealed that C. orbiculata was significantly more likely than chance to occur in a range

of land use classes in both the native and invaded ranges, but predominantly those with moderate to

high livestock density (Figure A.3). Urban land use classes were also statistically significant in all

areas. In New Zealand, Australia and the native range, the upper quartile of livestock density was

higher at C. orbiculata occurrence points than the overall background, especially noticeable for sheep

(Figure A.4). As this could be a sampling artefact due to higher overall sheep density in New Zealand,

the same analysis was run at Aeonium occurrence locations, and the same patterns did not occur (see

Figure A.5 and Figure A.6). In Australia the observed patterns may be biased by the large expanse of

desert, so no inferences should be made in this region. It is important to note that the FAO data are

coarse-scale, and that C. orbiculata also occurs on coastal cliffs and urban areas where livestock

density is zero, adding noise to the data.

To provide finer-scale analysis for New Zealand, the spatial intersection was redone using the New

Zealand Land Cover Database (LCDB) v4.0 (Ministry for the Environment & Landcare Research

2014) and farm type [Agribase Enhanced LCDB2TM

2006. (AsureQuality 2006)]. The LCDB classifies

land into 43 hierarchical classes based on broad characteristics (e.g. grassland, urban), with finer scale

sub-classifications (e.g. evergreen, urban parks), and is derived from satellite images taken between

2011 and 2013. Agribase, meanwhile, classifies farmland into categories (e.g. sheep grazing, dairy)

based on census data. These polygon layers were converted to 30 arc-second rasters to correspond

with occurrence data, using maximum combined area. The frequency of occurrences in each class

were tested for significance using the one-tailed binomial statistic with a p < 0.01 threshold. The

results were similar to the global analysis, although the class descriptions themselves are different. In

New Zealand, C. orbiculata was significantly likely to occur in both high-production grassland and

low production grassland, mixed exotic shrubland and built-up areas (Figure A.7a, Table A.3 for class

descriptions). The Agribase analysis showed that within agricultural land, C. orbiculata was

significantly likely to occur only in pasture grazed by sheep or mixed sheep and beef (Figure A.7b).

To create the habitat mask for C. orbiculata the statistically significant LCDBv4 classes were selected,

also including any classes that were directly comparable to statistically significant LUS global classes

(i.e. urban classes and bare ground, excluding snow and ice). Selected grid cells that fell within

farmland covered by Agribase were further constrained to include only sheep, or mixed sheep and beef

pasture. The resulting layer defined suitable land use classes. Because C. orbiculata occurs on cliffs

and outcrops as well as in vegetation (Webb et al. 1988), the suitable land use was merged with the a

priori layer used for Aeonium species, to create the final habitat suitability layer.

24

2.3.8 Model verification

Model goodness-of-fit was assessed by calculating sensitivity (the proportion of occurrence records

falling within cells modelled as suitable), both in New Zealand and globally. Sensitivity assesses

whether the modelled envelope is too conservative. BIOCLIM, by definition, will have high

sensitivity, perhaps at the cost of specificity (i.e. detection of true absences). A common problem in

modelling invasions is that the most commonly used statistics (e.g. AUC, Kappa) require generation of

pseudo-absence data and penalize models for predicting suitability where the species is currently

absent, despite the fact that not all absences are informative when modelling the potential distributions

of range-extending species (Soberón & Nakamura 2009).

To assess whether BIOCLIM was over-estimating climatic suitability, while avoiding generation of

pseudo-absence data and the attendant self-reinforcing consequences (Stokland et al. 2011; Golicher et

al. 2012), the same one-tailed binomial statistic as used in the land use analysis was calculated. This

statistic tests the statistical significance of sensitivity scores given the proportion of the model universe

projected as suitable (between 0 and 1), and estimates the probability of obtaining the observed

sensitivity or greater under a random model with the same projected suitable area. Statistics were

calculated for BIOCLIM models trained on both non-New Zealand data and all data. This compared

the effect of including New Zealand in the training data, where little difference in the projections with

and without the New Zealand data would indicate more stablity in projections. High sensitivity to the

inclusion of New Zealand data should warrant caution when interpreting the results, given that the

species may not be at equilibrium in the invaded range.

Models trained on global (non-New Zealand) data were validated against New Zealand data. For the

total models (world including New Zealand) training data had previously been split 80:20 for 5-fold

cross-validation, setting aside 20% of occurrences from each run for verification. The mean sensitivity

and p-values were calculated across all five runs. The final model (i.e. one run, trained on all available

data with no splitting), was compared with the total model for overlap. Statistics were also re-

calculated for the final model, after constraint by habitat suitability, against all New Zealand

occurrences. This was to quantify the difference in projected suitable area and whether habitat

constraint adversely affected model sensitivity.

25

2.4 Results

2.4.1 Niche analyses

In the niche analyses, principal components 1 and 2 accounted for 94%, 89% and 92% of variation in

the five bioclimatic variables for A. arboreum, A. haworthii and C. orbiculata, respectively. Principal

component 1 correlated positively with precipitation (primarily BIO17 and BIO19), except for

C. orbiculata where it was negatively correlated. Principal component 2 largely correlated negatively

with temperature (BIO10 and BIO11). Niche plots for all three species demonstrated clustered,

disjunct distributions in climatic space (Figure 2.2). The global occupied niche of C. orbiculata

represented a wider climatic range than either Aeonium species, while all three species’ occupied New

Zealand niches were similar and overlapped with the edges of the global niches to varying degrees. All

species’ New Zealand centroids were close to the climate most similar to that of the global distribution

(dry, mild climates), but generally, New Zealand represented an expansion of the occupied niche into

wetter conditions. None of the species occupy equivalent climates to the centroids of the New Zealand

niches elsewhere in the world, despite such environments being available.

All three species’ New Zealand niches were significantly different to the global distributions at the

95% confidence level (Table 2.1), in other words niche overlap (D) was lower than 95% of pooled and

randomly split occurrences. Furthermore, similarity p-values for A. haworthii between the global and

New Zealand niches were approaching 1, meaning that observed D was close to the mean of randomly

simulated niches. Only for A. arboreum was the observed global niche significantly more similar to

the New Zealand niche than random simulations.

Table 2.1 Niche equivalency and similarity of target species between global and New Zealand ranges,

following the methods of Broennimann et al. (2012). Similarity indicates whether niches in the target

ranges are more similar to each other than random simulations. Asterisks denote bootstrapped levels of

statistical significance of D (p ≤ 0.05), where they signify rejection of niche equivalency at the 95%

confidence level.

Species Equivalency (D) Similarity of world

niche to NZ (p-value)

Similarity of NZ niche

to world (p-value)

A. arboreum 0.38 * 0.06 0.02

A. haworthii 0.13 * 0.81 0.77

C. orbiculata 0.19 * 0.08 0.08

26

Figure 2.2 a-c) Kernel-smoothed PCA biplots of climatic niches, in the global range (red) and New Zealand range (blue), for a) Aeonium arboreum, b) A. haworthii

and c) Cotyledon orbiculata. Plots generated using 5 bioclimatic variables [(Hijmans et al. 2005), available at http://www.worldclim.org]. Solid lines delimit total

background climate, dashed lines delimit 50% of background climate. Shading indicates density of occurrences after kernel smoother applied. Correlation circles

show correlation between bioclimatic variables (see legend, g), with principal component axes for d) A. arboreum, e) A. haworthii and f) C. orbiculata.

(a) (b)

(d) (e) (f)

(c)

(g)


27

2.4.2 Performance of BIOCLIM models

In all cases, the sensitivity of BIOCLIM models trained on global data was lower than models trained

on 80% of total data (Table 2.2). Models trained on global data under-predicted suitable climate in

New Zealand, with only 5%, 2% and 29% of the country projected as climatically suitable for

A. arboreum, A. haworthii and C. orbiculata, respectively. While global models for both Aeonium

species correctly identified parts of the east coasts as suitable, notable areas where the species have

naturalized including Dunedin, Wellington and Auckland, were classified as unsuitable. The global

model for C. orbiculata performed better than for Aeonium species, but under-predicted in the North

Island, particularly the Bay of Plenty and Auckland. As expected, inclusion of New Zealand data

improved sensitivity and the cross-validated models performed significantly better than chance.

Models trained with New Zealand data had higher proportional projected suitable area both globally

and in New Zealand, a result of the New Zealand distributions representing an expansion of the

realized climatic envelope. The proportional projected suitable area of the final models (using total

data) was identical to the cross-validated models, and the two projections overlapped by 100% for all

three species. Global projections of final models (Figure 2.3) demonstrated narrow ranges of

climatically suitable conditions for both Aeonium species, with a high degree of overlap in

Mediterranean-type climates [i.e. warm temperate with dry summers (Peel et al. 2007)]. The global

projection for C. orbiculata shared similarities with both Aeonium species, but projected suitable area

was substantially higher, indicating broader climatic tolerances.

Table 2.2 Sensitivity (Sens.) and projected suitable area (PSA) of global (excluding New Zealand) and

total (global plus New Zealand) BIOCLIM models of Aeonium arboreum, A. haworthii and Cotyledon

orbiculata, tested against the world and New Zealand. Statistical significance of sensitivity, given

projected suitable area, calculated using Fisher’s one-tailed binomial statistic (* p<0.05, ** p<0.01).

Global models independently validated against New Zealand, total models cross-validated 5-fold

(mean value given).

Species Model World New Zealand

Sens. PSA Sens. PSA

A. arboreum Global 0.02 0.57** 0.05

Total 0.96** 0.03 0.93** 0.30

A. haworthii Global 0.01 0.16** 0.02

Total 0.98** 0.02 0.99** 0.45

C. orbiculata Global 0.13 0.91** 0.29

Total 0.99** 0.14 0.99** 0.60

28

Figure 2.3 BIOCLIM global projections of climate suitability, using all available data, for a) Aeonium

arboreum, b) A. haworthii and c) Cotyledon orbiculata. Model scores between 1 and 0 signify the

position within the n-dimensional climate space. Scores approaching 1 indicate similarity to the

species’ 50th percentile of the species’ rectilinear climate envelope (“core” climate), while 0 signifies

that the climate is outside the 5th or 95

th percentiles of the envelope.

29

2.4.3 New Zealand projections and habitat suitability

Projected suitable climate was concentrated primarily around the coastlines, but more prevalent in the

North Island than the comparatively colder South Island. In the South Island, projected suitable

climate was exclusively coastal for both Aeonium species, and restricted to the drier eastern side of the

Island for all three. BIOCLIM scores reflect distance to the 50th percentile in climate space, and should

not be interpreted as relative suitability because they are sensitive to biases in the training data.

However, the comparatively low New Zealand scores for C. orbiculata indicated that although the

projected suitable area was large, most of it is climatically similar to the outer extremes of the species’

distribution.

Masks of habitat suitability demonstrated lower availability of suitable habitat for Aeonium species

than for C. orbiculata, because C. orbiculata occupies a broader range (e.g. sheep pasture). The masks

demonstrated that there is suitable Aeonium habitat (e.g. cliffs) across much of New Zealand, albeit

patchily distributed. Suitable C. orbiculata habitat was not only less restricted than for Aeonium

species, but had higher connectivity in certain areas, particularly along the east coast. Constraining

BIOCLIM projections of climate suitability by habitat masks reduced the proportion of projected

suitable area in New Zealand for both Aeonium species by over 60% (Table 2.3). Projected suitability

for C. orbiculata was reduced by only 44% by habitat masks, with 34% of New Zealand still classified

as suitable. Sensitivity for the constrained models were slightly lower than climate-only projections

due to a small number of presences excluded by the masks (n = 7 for both Aeonium species, n = 2 for

C. orbiculata). This may have been due to incorrect geocoding, presence of unmapped microhabitats,

land use mosaics within grid cells or, potentially, exclusion of a suitable land use type.

Table 2.3 Projected suitable area (PSA) for Aeonium arboreum, A. haworthii and Cotyledon

orbiculata, with and without constraint by habitat. Sensitivity of constrained models shown with

significance calculated using Fisher’s one-tailed binomial statistic (** p < 0.01). Percent reduction in

projected suitable area, after habitat masks were applied, is given relative to climate-only models.

Species PSA

(unconstrained)

PSA

(constrained)

Sensitivity

(constrained)

% Reduction in

Suitable Area

A. arboreum 0.30 0.11 0.88** 62%

A. haworthii 0.45 0.15 0.90** 67%

C. orbiculata 0.60 0.34 0.99** 44%

30

Figure 2.4 a) New Zealand projections of final BIOCLIM climate-only models for Aeonium arboreum, with points showing occurrence records. Model (a) was then

constrained by (b), the mask of habitat suitability to give (c), the final projection of overall suitability. BIOCLIM scores are percentiles of the species’ distributions

in climate space. Scores approaching 1 indicate similarity to the species’ 50th percentile of the species’ rectilinear climate envelope (“core” climate), while 0 signifies



31

Figure 2.5 a) New Zealand projections of final BIOCLIM climate-only models for Aeonium haworthii, with points showing occurrence records. Model (a) was then

constrained by (b), the mask of habitat suitability to give (c), the final projection of overall suitability. BIOCLIM scores are percentiles of the species’ distributions

in climate space. Scores approaching 1 indicate similarity to the species’ 50th percentile of the species’ rectilinear climate envelope (“core” climate), while 0 signifies



32

Figure 2.6 a) New Zealand projections of final BIOCLIM climate-only models for Cotyledon orbiculata, with points showing occurrence records. Model (a) was

then constrained by (b), the mask of habitat suitability to give (c), the final projection of overall suitability. BIOCLIM scores are percentiles of the species’

distributions in climate space. Scores approaching 1 indicate similarity to the species’ 50th percentile of the species’ rectilinear climate envelope (“core” climate),

while 0 signifies that the climate is outside the 5th or 95


33

2.5 Discussion

Niche analyses confirmed disjunct distributions in climate space for all three species. The observed

“gaps” in climate space may be partially due to non-climatic limitation as a result of specific habitat

requirements of the species. Despite a small degree of niche overlap all three species occupy

significantly different climatic niches in New Zealand compared with the rest of the world, where New

Zealand represents an expansion into wetter conditions. The results of the niche analysis were

mirrored in the BIOCLIM projections where only models incorporating all global data performed

adequately in New Zealand, for any species. While some over-prediction in final models is to be

expected because of the nature of BIOCLIM and the use of few climate variables, projections indicate

that a large proportion of New Zealand is climatically matched to the species’ current ranges.

Constraining BIOCLIM projections by suitable habitat did not adversely affect model sensitivity, and

provided a more conservative projection of areas at risk of invasion by the three species. Although

final models are not a prediction of spread, they do provide valuable information for national weed

management, particularly regions where new incursions should be controlled, potential risk areas for

surveillance and the comparative threat posed by the different species.

2.5.1 What do the models reveal about the niche?

When including New Zealand in model training, projected suitable area increased dramatically for all

three species. This was especially true of A. haworthii, where the projected climatic niche expanded

from 2% to 45% of New Zealand when trained on all available data. The niche analyses demonstrated

the underlying cause. All three species’ occupied New Zealand niches are in considerably wetter

climates than elsewhere. In conjunction with the fact that similar climate is available in the global

background but unoccupied, a niche expansion in New Zealand is implied for all three species. It is,

however, impossible to determine through correlative methods alone whether it is an expansion of the

fundamental or the realized niche (Hulme & Barrett 2013; Guisan et al. 2014). Possible causes for

shifts in the fundamental niche include pre-adaptation to climates similar to the novel range in the

species’ evolutionary history (Petitpierre et al. 2012), exaptation (Gould & Vrba 1982), and

evolutionary change in the invaded range as a response to novel pressures or founder effects (Sax et al.

2007). Changes in the realized niche could arise from natural enemies (Keane & Crawley 2002) or

other non-climatic effects (González-Moreno et al. 2015), or phenotypic plasticity facilitating invasion

of novel climates (Price et al. 2003). Realized niche shifts might take the form of expansion in the

invaded range or un-filling in the native range [i.e. the species does not occupy all suitable climates

due to non-climatic factors, for example dispersal limitation; (Petitpierre et al. 2012)].

Regardless of the processes leading to the observed niche differences, an important consideration is

that the species’ current distributions in New Zealand could not have been adequately predicted prior

to their introduction. Global models performed better than chance and correctly identified some of the

invasion hotspots for the three species (Aeonium models correctly identified Banks Peninsula and

34

Napier as suitable, and the C. orbiculata model correctly identified most hotspots except those in the

wetter parts of the North Island e.g. Auckland). However, all three global models would have under-

estimated species’ distributions. Given the sensitivity of the models to the inclusion of the New

Zealand data, and the consequent increase in the potential distribution globally and nationally, the final

projections must be interpreted with caution. Despite the apparently wide potential distributions,

projections could be conservative if the species are not at equilibrium in New Zealand, and continued

spread further into novel climates cannot be discounted.

In contrast to Aeonium species, C. orbiculata had a noticeably wider projected suitable area, both with

and without the inclusion of New Zealand data. Cotyledon orbiculata occupies a diverse range of

climates in Southern Africa, which is a key factor in the projected climatic suitability of New Zealand.

Final models project suitable climate throughout the southern South Island and Central Otago [the

region closest to a continental climate in New Zealand, where some of the coldest temperatures in the

country have been recorded (MetService 2010)]. These surprising results are caused by a small

number of recorded presences in Lesotho at up to 3173 MASL, where minimum daily temperatures

are frequently sub-zero and seasonal and diurnal fluctuations can be extreme (Lesotho Meteorological

Services 2013). Although a high-elevation variety of C. orbiculata exists, it is not present in New

Zealand, and a local botanical expert in South Africa has confirmed that C. o. var. orbiculata (the

most widespread variety in New Zealand) is common at high elevation sites in Lesotho (Ernst Van

Jaarsveld, pers. comm., 2014). Freezing tolerance in C. orbiculata reportedly differs between coastal

and high-elevation populations, where plants from Lesotho can to avoid freezing damage to - 9.3 °C.

Crucially, this freezing avoidance may have a genetic basis as this trait persists after de-hardening

(Van Coller & Stock 1994). The cold tolerance limits of C. orbiculata in New Zealand may therefore

depend on the original source population of introduced plants. Removal of just 7 of the highest

elevation points in Lesotho resulted in a 23% reduction in projected suitable area in New Zealand

(Figure A.8). The climatic limits of C. orbiculata in New Zealand will therefore depend on whether

frost hardiness is an evolved genetic trait specific to Lesotho populations, or a result of pre-adaptation

or phenotypic plasticity, and the origins of New Zealand populations.

2.5.2 The role of non-climatic factors

The target species’ distributions are hypothesized to be restricted due to the effects of competition

avoidance, based on their highly specific habitat requirements and the low efficiency of CAM

photosynthesis relative to C3 and C4 plants. The two Aeonium species may achieve this primarily

through occupation of crevices in bare rock and other sparsely-vegetated habitats, based on the

species’ descriptions (Webb et al. 1988; Bramwell & Bramwell 1990). However, reports of stock

poisoning in the native range (Botha & Penrith 2008) and the U.S.A. (Fuller & McClintock 1988)

imply that C. orbiculata is also regularly found in pasture, a pattern which was confirmed by the land

use analysis (although occurrence records in the U.S.A. were in urban areas only). The tendency to

appear in grazed land was especially obvious in New Zealand data, and analyses indicated that this

35

was not a statistical artefact of higher overall grazing. Although grassland may seem at odds with

other C. orbiculata habitat (i.e. bare rock), this may also be a result of competition avoidance.

Cotyledon orbiculata produces bufadienolide cardiac glycosides, the toxic compound which results in

either immediate death, or the chronic disease known as “krimpsiekte”, in a number of animals

including sheep and cattle (Botha et al. 2007). The production of bufadienolide toxins is thought to be

a defence against ungulate herbivory (Van Jaarsveld & Koutnik 2004), thereby allowing populations

to establish in pasture while other would-be-competitors are grazed.

There are examples of other Crassulaceae benefitting indirectly from the presence of herbivores via

consumption avoidance. Experimental manipulation of vertebrate grazing pressure on Crassula

helmsii (Kirk) Cockayne in the U.K. found that cover increased in the presence of sheep and buffalo

due to the removal of competitors (Dean et al. 2015). Bryophyllum delagoense (Ecklon & Zeyher)

Schinz contains the same toxic compounds as C. orbiculata and is a serious pest of grazing land in

Australia (Witt 2004), although low frequency and intensity of fires in grazed land may also contribute

to spread (Witt & Nongogo 2011). It is unclear whether fire is also important for C. orbiculata, and

this cannot be discounted as a potential contributing factor to spread. Roadside spread of

B. delagoense in Australia has been exacerbated by the use of mechanical slashers that simultaneously

spread its seeds and plantlets and reduce competition from other species (Department of Agriculture

and Fisheries 2013). The functional similarity of slashing to ungulate herbivory suggests that

B. delagoense could be exapted to disturbance by herbivores. Meanwhile, many other species in the

Cotyledonoideae clade produce the same toxic compounds as C. orbiculata (van Ham 1995; Mort et

al. 2005), all of which evolved in South Africa. The region’s dry climate and many large native

herbivores may elicit strong selective pressure, and evolved grazing avoidance or tolerance could

explain why some South African Crassulaceae species have been shown to increase cover in the

presence of elephants (Moolman & Cowling 1994). Aeonium species, in contrast, evolved in the

Canary Islands where the only large native herbivore is the giant tortoise, therefore they have not

evolved herbivore defences (Jorgensen & Olesen 2001). It is possible, then, that similar processes

have been conducive to the spread of C. orbiculata in New Zealand sheep pasture, specifically grazing

avoidance and re-rooting from broken material, easily caused by vertebrate trampling (JP, personal

observation). What the analyses were not able to determine is whether grazing intensity is important in

determining C. orbiculata distributions, a question better addressed with experimental techniques.

2.5.3 Potential distributions in New Zealand

Model projections indicated that a large proportion of the North Island and east coast of the South

Island is climatically favourable for all three species. However, constraint by suitable habitat strongly

reduced projected suitable area. This was especially the case for Aeonium species, where over 60% of

climatically suitable area was excluded based on non-climatic factors. The reduction in climatically

suitable area for C. orbiculata was only 44%, but indicates that land use may still constrain potential

distributions considerably.

36

The strong reduction of suitable habitat for Aeonium species does not exclude the possibility of

suitable microhabitats in other grid cells, or the fact that the realized distribution may be further

constrained by other factors e.g. geology. For example, in Canterbury in the South Island riparian

cliffs were classified as potential habitat, but it is unknown whether the alluvial sediment of the region

(G.N.S. Science 2014) might be suitable for Aeonium species. Assuming, then, that final models most

likely over-predict in New Zealand, the availability of suitable Aeonium habitat can be assumed to be

low unless the species are able invade habitats other than where they have been previously described.

It is unlikely that Aeonium species would be capable of invading pasture as C. orbiculata has, as they

do not have herbivore defences and succulents are otherwise high-quality forage in dry environments

(Moolman & Cowling 1994). Aeonium species are thus likely to be more restricted by availability of

suitable land forms (e.g. cliffs) than by climate in New Zealand, but if the climatic niche continues to

expand other rocky habitats could become vulnerable, potentially threatening native species that also

use rock outcrops as refugia (Wiser & Buxton 2009).

Cotyledon orbiculata, conversely, has little shortage projected suitable habitat. Further expansion of

the climate envelope in New Zealand would thus likely have a greater effect on the potential

distribution of C. orbiculata than Aeonium species. However, as with the Aeonium species, projections

could be further refined by additional non-climatic factors, e.g. soil type. Attempts to use spatial

intersection techniques for soil type with C. orbiculata were unsuccessful, presumably because the

species is found on a wide range of soils (Van Jaarsveld & Koutnik 2004), and where the species

occurs on bare rock the surrounding soil type is irrelevant. To understand the importance of other non-

climatic factors, experimental techniques could be informative. Nonetheless, the risk posed by

C. orbiculata to New Zealand is highly dependent on climatic suitability, which as discussed, is

uncertain depending on the source of introduction and degree of non-equilibrium in New Zealand.

2.5.4 Limitations

An SDM is, at best, an approximation of reality. I aimed to estimate the extent of climatically suitable

habitat in New Zealand for the three species, and the limitation of their potential distributions by non-

climatic factors. In reality, the species’ distributions will be constrained further by additional factors

not included in final projections, for example topology, geology, soil, biotic interactions and dispersal.

As discussed, teasing apart the influences of these factors on the species’ distributions may be more

suited to experimental techniques at a finer scale and is a worthwhile avenue for further study.

Additionally, testing all three species’ climatic limits in the invaded range would provide valuable

insight into their potential to continue spreading into novel climates.

It is important to consider model uncertainty arising from spatial scale (grain size), model type and the

quality of input data. Potential habitat was modelled at a 30 arc-second scale (approximately 1 km2),

so variation in climate and land use within “unsuitable” grid cells may give rise to suitable

microhabitats. The model BIOCLIM, while useful for this study, is particularly prone to over-

37

prediction relative to other SDMs (Tessarolo et al. 2014). Furthermore, the Worldclim bioclimatic

layers used are interpolated and averaged from weather station data over a 30 or 50-year period

depending on location (Hijmans et al. 2005). The variables therefore mask inter-annual variation and

climatic extremes that may be limiting. Other climate variables only indirectly represented by the

Worldclim data may be more biologically meaningful for the species, e.g. frost or growing degree

days. Finally, while use of pseudo-absence data in model validation was avoided, there remains no

way to fully validate SDM outputs without independent data including true absences (i.e. where it is

certain that the species does not occur). The final models therefore are likely to over-predict habitat

suitability, and represent a “worst-case” scenario of potential distributions. This list of assumptions is

not exhaustive, and I emphasize that model projections, as with any SDM, should be interpreted with

these caveats in mind.

2.5.5 Conclusions

I show that A. arboreum, A. haworthii and C. orbiculata occupy novel climate space in their invaded

ranges in New Zealand, constituting a shift in the occupied niche towards wetter climates. BIOCLIM

projections trained on all known occurrences project a high proportion of New Zealand as climatically

suitable for all three species, and therefore spread can be expected to continue. Accounting for non-

climatic limitation dramatically reduces all three species’ potential distributions in New Zealand,

especially Aeonium species. Relative to the Aeonium species, it is clear that C. orbiculata poses a

greater threat to biodiversity and productive ecosystems in New Zealand.

38

Chapter 3 – Testing performance along an elevation gradient

reveals the climatic limits of alien Crassulaceae in New Zealand

3.1 Abstract

Predicting climatic limits and potential distributions of non-native plants is a rapidly growing

discipline. Correlative or observational approaches are commonly employed to predict limits but they

usually assume that species are at climatic equilibrium, and this condition is rarely fulfilled. To

confidently project climatic limitation an understanding of how far the species is from equilibrium is

necessary, especially in the introduced range where non-equilibrium may be exaggerated. Yet, few

studies experimentally test climatic limits in the introduced range. Fewer still go on to predict plant

performance beyond current range limits. In this study I experimentally test vital rates, in response to

climate, of three non-native plant species in New Zealand. By transplanting cuttings and seeds of

Aeonium arboreum, A. haworthii and Cotyledon orbiculata over a gradient of 0 - 700 MASL in the

Banks Peninsula region, seedling establishment, growth and mortality are quantified in response to

climate, within and beyond species’ range limits. Performance was measured over two years and

observed vital rates modelled against climatic variables, using the resulting functions to predict

performance up to 300 m above current range limits. Results are used to infer whether the species have

reached their climatic limits, and whether spread to higher elevations is likely. There is evidence that

all three species are strongly climate-limited on Banks Peninsula, and that high elevations are

detrimental to plant performance. All species appear close to their climatic limits in the region,

particularly Aeonium species, which are likely to be confined to around 300 - 400 MASL. Aeonium

species are limited at high elevations by reduced growth and seedling establishment, and higher

mortality. Cotyledon orbiculata poses a greater risk to the region than Aeonium species as it is already

present at higher elevations, and there is less consensus between predicted vital rates at higher

elevations. Cotyledon orbiculata appears to be primarily limited by relative growth and upward spread

cannot be discounted, although such populations would likely be marginal. This is the first study of

climatic limitation of the three species in any introduced range, and provides key information for

assessing their potential distributions in New Zealand.

Keywords: climate, elevation, transplant, invasion, Crassulaceae

3.2 Introduction

Untangling drivers of invasive species’ distributions and predicting potential spread is a prominent

area of ecological research (Guisan & Thuiller 2005). Once a species has established in an introduced

range, determining the extent to which it may spread is a complex and often uncertain process (Wilson

et al. 2007; Bradley et al. 2010) that relies on knowledge of the species’ climatic limits. It is generally

accepted that species’ distributions are limited by numerous factors that are scaled hierarchically

39

(Mackey & Lindenmayer 2001); ultimately, climate is thought to limit ranges at the coarsest grain and

largest extent (Woodward 1987), with other factors, e.g. biotic interactions, limiting distributions at

finer grains and in smaller regions (Collingham et al. 2000; Guisan & Thuiller 2005). Therefore, to

assess potential spread of a non-native plant in its introduced range its climatic tolerances must first be

determined, as this will define its coarsest distribution limits.

Measuring species’ responses along elevation gradients is a useful proxy for investigating climatic

limitation. Elevation is a strong determinant of plant distributions (DeFerrari & Naiman 1994) and

many species have well-defined limits. Species richness generally declines as elevation increases

(Marini et al. 2009). Furthermore, elevation limits are often stable between species’ native and

introduced ranges, and correspond well with their climatic tolerances (Alexander, Naylor, et al. 2009).

Studies along elevation gradients are also practical as they allow us to measure responses to a wide

range of climates over a small study area (Haider et al. 2011). Climatically, high elevations exhibit

cooler temperatures, more frequent frosts and shorter growing seasons, and are overall less conducive

to plant performance (Körner 2007). It is difficult, however, to determine which causal effects shape

distributions along elevation gradients without experimental approaches. While high elevations are

generally less favourable for plant growth and performance, there are multiple contributing factors not

necessarily related to physiological limits that may be confounded by observational methods.

Numerous non-climatic factors affect performance at high elevations: soil quality is often poorer,

disturbance regimes altered, physical area reduced, and land use may change (Körner 2007; Pauchard

et al. 2009). Further, propagule pressure may diminish due to the gravitational difficulty of dispersing

uphill and reduced anthropogenic activity (Marini et al. 2009; Alexander et al. 2011), and biotic

interactions may change (Badano et al. 2007). Therefore, while purely observational or correlative

studies often identify that elevation is a determinant of non-native species richness (Pauchard &

Alaback 2004), the underlying mechanisms may be clouded as they cannot standardize for non-

climatic effects. In contrast, experiments testing performance along elevation gradients provide

opportunities to identify the extent of climatic limitation and the relative importance of individual

variables (Paiaro et al. 2007; Leger et al. 2009).

Studies of species’ climatic limits also benefit from looking beyond just presence-absence data into the

underlying demographic processes driving limitation (Hastings et al. 2005). Demographic processes

(i.e. population mortality, fecundity) determine whether plants can colonize and form self-sustaining

populations, and each individual vital rate (e.g. germination, survival) may be differentially influenced

by a multitude of climatic and non-climatic drivers [e.g. Baret et al. (2004)]. Vital rates may vary

within populations due to genetic effects, microhabitat factors and biotic interactions (Sexton et al.

2009), and between populations due to larger scale climatic, environmental or biotic effects (Kollmann

& Bañuelos 2004; Leger et al. 2009). They may also vary within individuals because of time-

dependent effects, such as ontogenetic drift (McConnaughay & Coleman 1999). Classifying habitat

suitability without knowledge of underlying processes may be misleading (Haider et al. 2011). If the

40

climate is sufficient for survival but not germination, populations may be inexplicably absent.

Similarly, sink populations may exist where conditions are sufficient for germination and survival, but

not reproduction (Willis & Hulme 2002; Baret et al. 2004).

A further reason to experimentally investigate non-native species’ climatic limits is that invasions are

sometimes characterized by non-equilibrium. While a species at geographic equilibrium occupies all

potentially suitable habitat (Hutchinson 1957), this condition is rarely fulfilled due to non-climatic

factors that limit dispersal (Brown et al. 1996). More importantly, non-equilibrium may be particularly

extreme during invasions (Thuiller et al. 2006; Wilson et al. 2007), where the species’ range of

occupied habitats may not be indicative of its full tolerances. This can be caused by invasion lags,

where the invader remains at low prevalence for a number of years following introduction (Aikio et al.

2010), and anthropogenic effects such as human population density (Pyšek et al. 2010), among other

factors. Yet, the most popular methods for predicting non-native species’ climatic limits are

correlative (Guisan & Thuiller 2005; Araújo & Peterson 2012; Ahmed et al. 2015), and most assume

equilibrium in the training range (Elith et al. 2010). Correlative approaches may produce unreliable

predictions in non-equilibrium situations and over or under-estimate the risk of spread (Varela et al.

2009; Václavík & Meentemeyer 2012), and only experimental approaches can test whether the

assumption of equilibrium holds true. Despite these problems, studies that measure non-native species’

vital rates across climate gradients (Alexander, Edwards, et al. 2009; Seipel et al. 2015; Walter et al.

2015), or use experimental methods to test climatic limits (Willis & Hulme 2002; Angert & Schemske

2005; Griffith & Watson 2006; Leger et al. 2009), are relatively rare. Even fewer go on to make

explicit predictions (Ross et al. 2008), and many lack the experimental design necessary to strongly

infer species’ range limits (Hargreaves et al. 2014).

In this chapter, I investigate the climatic responses of three succulent plants over part of their

introduced ranges in New Zealand. Cuttings and seeds of Aeonium arboreum, A. haworthii and

Cotyledon orbiculata were transplanted within and beyond their current elevation limits on Banks

Peninsula, an invasion hotspot for all three species south of Christchurch. The topography provided a

steep elevation gradient, ranging from evidently climatically suitable along the coastline, to beyond

their hypothesized climatic tolerances at the inland peaks. All three species occur predominantly at

low elevations near coastlines, and since naturalization in the late 19th century, they have spread along

coasts and upwards to around 400 MASL. The three species are strongly limited by non-climatic

factors; they prefer bare substrate (e.g. cliffs), and C. orbiculata can colonize sparse grasslands (Webb

et al. 1988). It is particularly difficult to infer climatic requirements using observational data when

suitable habitat is restricted (Brown et al. 1996), therefore it was necessary to experimentally test the

species’ climate limits to assess potential spread. Climatic factors influencing growth, mortality and

germination are modelled, and used to infer the likelihood of spread to higher elevations. This study is

the first to quantify the climatic responses of these species and link it to their invasive potential.

41

3.2.1 Aims

1. Using a field experiment along an elevation gradient, to test whether current distribution limits

on Banks Peninsula of A. arboreum, A. haworthii, and C. orbiculata represent the climatic

limits of the species.

2. To identify which vital rates (mortality, growth and seedling establishment) are most limiting

to continued upward spread in the region, by quantifying their responses to climate.

3. To examine the potential for the species to continue spreading in the region by comparing

predicted vital rates at high elevations on Banks Peninsula to predictions at their current

elevation limits.

3.3 Methods

3.3.1 Study species

Aeonium arboreum, A. haworthii and C. orbiculata are succulent long-lived perennials in the family

Crassulaceae. These species were chosen because they are thought to be strongly restricted by habitat

and climate in New Zealand, are potential environmental weeds, and there is evidence that they may

not have reached equilibrium (Chapter 2). In their native ranges, all three species occupy relatively

warm, dry environments (Table 3.1), but how their reproduction, growth and survival respond to

climate is uncertain. All three are polycarpic, producing multiple compound inflorescences in summer,

with the resulting wind-dispersed seeds germinating the following spring (Alamo et al. 1996;

Zietsman 1998). Little is known about their germination capabilities or optimal conditions, though

there are reports of between 0 and 84% germination, and optimal temperatures between 16 and 24 °C,

in closely related species (Alamo et al. 1996; Daws et al. 2007; Royal Horticultural Society 2014).

Although all three species currently occur at lower elevations in New Zealand than in their native

ranges, the climates of the New Zealand distributions are wetter and cooler (Table 3.1). Their climatic

limits are particularly unclear as CAM photosynthesis is often associated with phenotypic plasticity

and flexible niche occupation (Luttge 2004). In general, all three species are drought tolerant and

C. orbiculata can withstand fluctuating periods of drought and high rainfall (Eller & Ferrari 1997).

They require free-draining soil and dry climates (Vogan 2003), with some precipitation during the

growing season (Jorgensen & Olesen 2000; Royal Horticultural Society 2014), prefer sunny aspects

with minimal shade (Vogan 2003), and C. orbiculata may be somewhat adaptable to solar radiation

intensity as it can regulate its photoprotective epicuticular wax in response to light levels (Barker et al.

1997). The high water content of these species, up to 95% for C. orbiculata (Eller & Ferrari 1997),

may result in frost sensitivity. However, there is conflicting evidence of freezing avoidance, with

sources reporting minimum temperatures ranging between 5 °C and - 9.8 °C (Lösch & Kappen 1981;

Van Coller & Stock 1994; Vogan 2003; Royal Horticultural Society 2014). In addition, high levels of

flavonoid agylcones in Aeonium species may aid robustness to climatic stress (Stevens 1995).

42

3.3.2 Study area

This chapter focusses on Banks Peninsula, a volcanic region of 1150 km2 directly south of

Christchurch, New Zealand between latitudes - 43.56 and - 43.90 decimal degrees, and longitudes

172.38 and 173.13 (WGS 1984). The terrain of Banks Peninsula results in a steep climatic gradient

(Boffa Miskell 2007), with four distinct bioclimatic zones based on distance to the coast and elevation

(Wilson 1993). Annual rainfall varies between 600 mm per annum (p.a.) in the drier northern bays, to

2000 mm p.a. in the southern valleys (Figure 3.1). Mount Herbert is the highest peak at 919 MASL,

and while temperatures are mild at low elevations, the hilltops are temporarily snow-covered during

most winters (Soons et al. 2002). I expected the elevation gradient on Banks Peninsula to encompass

climatic conditions ranging from suitable to unsuitable for the study species. Climate is likely to be the

primary limiting factor on Banks Peninsula, as suitable habitat is abundant; the volcanic landscape

forms abundant cliffs and outcrops, preferred habitat for all three species, and the primary land use in

the region is sheep pasture (Boffa Miskell 2007), suitable for C. orbiculata. Current occurrence

records of all three species are concentrated in the northern bays at low elevations (Figure B.1),

confined to the warmest, driest parts of the region, though C. orbiculata occupies a wider climatic

range than the two Aeonium species (Figure B.2)

3.3.3 Experimental design

Growth, survival and germination of the three species were tested by transplanting cuttings and seeds

at 40 field sites on Banks Peninsula. Sites were placed between 7 and 681 MASL at varying distances

to the coast, within and beyond the species’ current limits. A preliminary power analysis was

conducted to estimate the necessary degree of replication, and based on the results each site contained

five cuttings and 300 seeds of each species (a total of 15 plants and 900 seeds). Raster maps of climate

[500 m, (Tait 2007)] were then used to classify grid cells on Banks Peninsula according to annual

average air temperature (Temp) and average summer precipitation (Rain). Averages were calculated

over 1971 – 2009. Each cell was assigned into one of five categories using equation 1,

where 𝜇 = mean for Banks Peninsula, and 𝜎 = standard deviation. Grid cells were divided into five

categrories, from cold and wet, to hot and dry, by ranking the climate index.

Climate index = [(Temp - 𝜇Temp) – 𝜎Temp] - [(Rain - 𝜇Rain) - 𝜎Rain] (1)

Field sites were located within Christchurch City Council reserves because public land was more

easily accessible, it was more straightforward to gain the necessary permissions, and the Council were

highly supportive of the work. Sites were selected by dividing available council reserves into the range

of climate index categories within, and selecting individual sites no less than 50 m apart, attempting to

evenly represent both the climate indices and elevation (between the lowest and highest points in each

reserve, and overall between sea level and the maximum elevation possible). Three of the four

bioclimate zones on Banks Peninsula (Wilson 1993) were represented in the design (Table 3.2). I also

43

attempted to represent aspect evenly (cardinal directions N, E, S, W), but because accessibility was

limiting neither elevation nor aspect are perfectly balanced. Following the Christchurch earthquake in

February 2011, it was necessary to select an additional seven sites for germination trials (see section

3.3.5 for details). Full site details are provided in Table B.2.

3.3.4 Growth and mortality experiment

The second aim of this chapter was to identify which vital rates are most likely to limit upward spread.

Growth and mortality were tested by transplanting cuttings to sites, and seeds were transplanted to

measure germination (section 3.3.5). In October 2010, I sourced 220 cuttings from 11 naturalized

Banks Peninsula populations per species (total = 660 cuttings), attempting to sample as wide a range

of occupied climates as possible (Figure B.1). This allowed investigation of potential source effects on

performance (after de-hardening), where differential responses could suggest local adaptation. When

collecting cuttings I took at least one apical leaf pair for C. orbiculata and at least one terminal rosette

with 5 cm of stem for Aeonium species. Cuttings were planted in trays of sterilized pumice within 12

hours of collection, dipping stems into Seradix™ rooting powder (active ingredient 0.1% 4-indole-3-

butyric acid) beforehand. After two weeks’ cultivation in glasshouse conditions, cuttings were planted

into individual 0.9 L pots containing seedling potting mix; a 3:2 mix of peat and pumice, with 200 g

dolomite, 50 g soil wetting agent (Hydraflo L® ), and 100 g slow-release fertilizer (Osmocote

® Exact

Mini 3-4M) per 50 L. During planting, root length was measured. Cuttings were cultivated in

glasshouse conditions for a further four weeks before transferring outside for two weeks to minimise

shock before transplantation. Before transferring plants to the field, their heights and widths (mm)

were measured as a baseline.

In November 2010, the beginning of the three species’ flowering seasons, plants were transferred to

the field sites. Cuttings were individually and randomly assigned to sites, first excluding the 20 with

shortest root lengths. On transplanting, individuals were placed approximately 15 cm apart, in pots,

into holes of 10 cm depth. Pots were arranged in a grid of 5 rows by 3 columns, each column

comprising a single species, rotating the order of species’ columns at each new site. To record air

temperature, one Thermochron® iButton data logger was placed facing south in the central pot of each

site, 5 cm above ground level with a cover of aluminium foil to protect from precipitation and solar

radiation. Data loggers were programmed to record temperature every four hours to the nearest 0.5 °C.

I measured aspect at each site to the nearest cardinal direction (N, E, S, W or NA on flat terrain), and

vegetation canopy cover using a convex spherical densiometer (Forestry Suppliers Inc., model 43887),

according to the methods of Lemmon (1956). Canopy measurements were taken from 50 cm above

ground at four cardinal directions (N, E, S, and W), and averaged to give percentage overhead density.

To protect from livestock, a steel cage measuring 1 × 1.5 × 0.8 m was secured over the cuttings.

44

Table 3.1 Target species traits. Maximum size and time to maximum size from Vogan (2003) and Royal Horticultural Society (2014). Elevation, precipitation and

annual mean temperature in native, New Zealand, and all other introduced ranges taken from occurrence data (Table A.1) and Worldclim Bioclim variables

[(Hijmans et al. 2005), available at http://www.worldclim.org]. Minimum elevation for all species in all regions is 0 MASL.

Species Native range Growth

form

Max size (cm) Time to

max size

(years)

Max elevation

(MASL.)

Annual precip. (mm) Annual mean temp. (°C)

Native NZ Other Native NZ Other Native NZ Other

A. arboreum Morocco Upright 180 tall 5-10 1600 200 1000 100-6000 600-1500 300-1200 12-20 10-15 11-20

A. haworthii Canary Islands Mounding 60 tall 80 wide 10-20 900 400 500 300-5000 600-2200 300-1000 15-21 10-16 12-19

C. orbiculata Southern Africa Upright 150 tall Unknown 2700 400 700 0-1100 600-1800 300-9000 18-23 10-15 11-20

Table 3.2 Number of sites on Banks Peninsula used for cuttings only, seed trays only, or both, in each bioclimate zone as defined by Wilson (1993).

Elevation (MASL) Wilson (1993) bioclimate zone Number of sites

Cuttings only Seeds only Both

000 - 150 Maritime cool temperate (coastal) 4 6 8

150 - 500 Lower cool temperate * 3 1 16

500 - 750 Upper cool temperate 0 0 9

750 - 900 Subalpine 0 0 0

* 0-100 MASL inland


45

Figure 3.1 a) Field sites, and weather stations providing precipitation data, b) field site elevations, and

c) location of Banks Peninsula. Field sites contained cuttings only, seeds only or both (see legend), site

numbers correspond to Table B.2 (site details). Base map is total annual precipitation with shaded

relief, where grey indicates no data. Precipitation was interpolated from the 30 arc-second Worldclim

layer [(Hijmans et al. 2005), available at http://www.worldclim.org].


46

3.3.5 Germination and seedling survival experiment

Germination and seedling survival was assessed by transplanting seed trays to experimental sites and

monitoring for one year. Seed was sourced in 2011 from wild inflorescences, harvested from eight

distinct populations per species (Figure B.1) from a range of climates to test for possible source

effects. Pods were emptied and the contents homogenised into one mixed sample per source

population. Differences in seed size between Aeonium species and C. orbiculata required that

Aeonium seeds were sown by weight, while C. orbiculata seeds were visible to the naked eye and

were sown by hand. Due to the small size of Aeonium seeds, a 0.1 g sample of mixed seed and chaff

from each source population was weighed (to the nearest 100 µg), sorted under a dissection

microscope at 10 × magnification, and all seed counted to estimate the weight (g) of 100 seeds. This

amount was weighed and subdivided equally into ten samples, assumed to contain approximately ten

seeds (Table B.3). I tested baseline seed viability in order to account for any effect of seed source on

germination. Samples of 100 seeds were drawn from each of the mixed samples used for sowing, and

suspended in 5 ml of triphenyl tetrazolium chloride (TTC) solution inside a sealed test tube. The TTC

was dissolved in deionized water at 1%. Test tubes were kept in the dark at 21 °C for 36 hours, after

which point seeds were individually examined under the microscope at 40 × magnification. Seed coats

were removed with a needle. The TTC is a redox indicator that reacts with tissue exhibiting cellular

respiration, and is used to assess viability, vigour and malformed embryos (Leist & Krämer 2003).

Darker staining indicates more vigour, while partially stained seeds indicate non-viability of the

cotyledon or radicle and therefore malformation, while absence of staining indicates non-viability.

Each seed was categorized as high vigour, low vigour, malformed or non-viable (Figure B.3), and

summed over each site to give a percentage for each category.

Seeds were sown into germination trays and transported to the field in July 2011 (the austral winter),

to allow dormancy to be broken naturally prior to germination in spring. Seeds were planted into cell

trays of 9 columns by 10 rows, where each cell had a 10 ml capacity. Trays were subdivided into 3

blocks of 3 columns (one block per species), and the order of blocks was rotated at each site. Each

column corresponded to one source population, assigned with a stratified design evenly representing

sources across elevations. A total of 900 seeds were sown in each tray, with approximately 10 seeds in

each cell. The same standard seedling potting mix was used as for plant cuttings. To minimise risk of

seed escape, trays were covered with a fine-gauge mesh, white to prevent artificial warming via solar

absorption. Because of an earthquake on February 22nd

2011, seven sites were inaccessible for over

one year and so could not receive seed trays. Instead, six volunteers offered the use of private

residential gardens on Banks Peninsula and these were used as replacement sites, as well as one

additional site provided by the Christchurch City Council. These seven sites were used for germination

trials only (Figure 3.1).

47

3.3.6 Risk mitigation and site monitoring

Cotyledon orbiculata is an Unwanted Organism in New Zealand, therefore propagating the organism

requires an exemption from the Ministry for Primary Industries (MPI). Permission was granted under

the condition that all plant material was transported securely, had minimal chance of escape or

reproduction, and was destroyed in November 2012. Cuttings remained in place for two years and

were monitored every four to six weeks over spring and summer, and every three months during

autumn and winter. Visits were to check for inflorescences, to ensure that data loggers were

functioning, and to record mortality. I allowed inflorescences to develop and counted emerging

flowers, but removed them before seeding. Plants were measured every 6 months at the end of

November and beginning of June, recording aboveground canopy volume (height, width and length) in

millimetres. Seedlings were counted at each visit for the first three months after planting to capture

emergence and mortality, then afterwards at the normal 6 - monthly measurement intervals. When the

experiment ended in November 2012, plants and seed trays were sprayed with one of six herbicides:

glyphosate, picloram, or metsulfuron, each with or without additional penetrant. One month later, all

roots and plant material were removed and destroyed, and the soil was re-sprayed with the most

effective of the herbicides (see Appendix E). Annual site monitoring continued until November 2015.

3.3.7 Analysis and environmental variables

Seedling establishment, and plant growth and mortality were modelled using generalized linear mixed

models (GLMMs) in the R package lme4 (Bates et al. 2014; R Core Team 2014), as a function of

environmental variables. To account for pseudo-replication, the variables Site (field site) and Source

(plant/seed source population) were included as crossed random effects in all models. Eight

environmental variables were used, calculated as annual or six-monthly means depending on the

response variable. Variables were added as linear fixed effects except where otherwise stated, first

testing for significant effects of variables individually, then fitting a model with all significant effects

and removing non-significant redundant variables in a stepwise fashion, testing for improvement in

AIC at each step using a Chi-squared test using the anova function in R’s base package. I also tested

for potential interaction effects between significant variables. Models were tested against a null model

with random effects only, also with a Chi-squared test. All model coefficients are reported with 95%

confidence intervals, calculated with the confint.merMod function using 500 bootstrapped replicates.

Eight environmental variables were used to explain variation in plant performance. Solar radiation

(KWh/m2) was included on the basis that sunlight is fundamental to photosynthesis and plant growth

(Monteith 1972), and was modelled using the Solar Radiation Spatial Analyst tool in ArcMap 10.1 (Fu

& Rich 1999; Environmental Systems Research Institute 2011) with a 15 m DEM base layer. Growing

degree days (GDD) and frost days (minimum temperature below 0 °C) were included as plants

generally respond to heat sums (Bonhomme 2000) and because the species are believed to be frost

sensitive (Vogan 2003). I calculated GDD at bases 5 and 10 °C using the raw four-hourly temperature

48

data from the site data loggers (see section 3.3.4). Bases 5 and 10 were chosen despite being correlated

(r = 0.88), because it was unknown which temperature would be most biologically relevant to the

species. Total precipitation (mm) was included because high rainfall is likely to be limiting to

xerophytes. Data were obtained from the nearest weather station in the CliFlo database [n = 7, Figure

3.1, (National Institute of Water and Atmospheric Research 2014)]. Limitations are discussed in

section 3.3.10. Aspect was included as a categorical variable of the nearest cardinal direction (NA on

flat terrain), because occurrence data indicate that most populations are on north-facing slopes, and, in

the event that modelled solar radiation did not accurately reflect site conditions aspect would be a

crude proxy. Elevation (MASL) was included to capture any unexplained variation along the

experimental gradient, and overhead canopy cover (%) was included as the species are thought to be

shade-intolerant (Vogan 2003). Canopy cover (CC) was calculated from spherical densiometer

readings (see section 3.3.4). All climatic variables were standardized to a mean of zero and standard

deviation of one to allow comparison of effect sizes where data are measured on different scales.

3.3.8 Model fitting and performance

Models of germination, mortality and growth were each fitted separately with varying time steps for

environmental variables. Germination was modelled as the total number of seedlings in November

2012 out of 100 seeds originally sown, fitted with a logistic GLMM. This model accounted for

germination and subsequent survival, over approximately the same annual time step as other models,

and is hereafter referred to as “seedling establishment”. While a survival analysis would also be

appropriate for these data, it was decided to maximize simplicity to facilitate later extrapolation.

Although some emergence occurred in September (Figure 3.2), climate variables were summed over

an annual time step (November - November) rather than, for example, July 2011 - November 2012, to

allow comparison of predictions with other vital rates. Climate variables were highly correlated

between 12 and 17-month sums, thus choice of time step did not affect model performance.

Relative growth between each measurement interval was calculated from estimates of aboveground

canopy volume (height × width × length, reported hereafter in litres). Relative growth standardises for

differences in raw volumes, and was calculated according to equation 2.

Relative Growth = [ln (Volumet+1) – ln (Volumet)] (2)

Annual relative growth in years one and two was modelled as a Gaussian GLMM over a November -

November time step. Although growth varied throughout the year, net annual growth was modelled

rather than seasonal growth, because it is likely to be more relevant to the species’ climatic limits.

Additionally, predictions were considerably easier to interpret, and simplicity was preferable for

extrapolating model predictions. In addition to all aforementioned climate variables, a quadratic

elevation term was included in the growth models because scatterplots indicated a clear quadratic

relationship between relative growth and elevation. Year was included as a fixed factor effect due to

49

lower relative growth over time at all sites. This assumes the same slope in the relationship between

growth and climate, but fits a different intercept for each year. To test the validity of this assumption I

ran single-year models of annual relative growth, and found similar effect sizes for the same climate

variables as in the two-year model. Plotting relative growth against significant variables revealed

similar gradients over both years, but with different intercepts (Figure B.4).

Mortality was modelled using two distinct 6 - monthly models, as survival patterns were highly

seasonal. Logistic models were run using the binomial response variable, dead/alive, for individual

plants. One model was run for “summer” (December 1st - May 31

st) and one for “winter” (June 1

st -

November 31st). There were two years of observations for the winter models, but only one for summer

due to zero deaths in the first 6 months. Summer mortality therefore had insufficient replication to be

modelled using a GLMM, and was instead modelled using a binomial GLM without random effects.

The additional variable, canopy volume at the time of last measurement (six months previously), was

included for all mortality models under the hypothesis that small plants had higher risk of mortality.

Canopy volume (v) was log-standardized according to equation 3 (�̅� = mean, s = standard deviation).

Log Standardized Canopy Volume = {ln [vi] - �̅� [ln (v)]}/{2s [ln (v)]} (3)

To test degree of fit in final models, marginal and conditional R2 were calculated using a function

based on the methods of Johnson (2014), which estimates a pseudo-R2 using fixed effects only and all

effects, respectively. I calculated McFadden’s pseudo-R2 (McFadden 1973) for the simple binomial

models of summer mortality. In addition, prediction of binary outcomes for seedling and mortality

models was assessed using area under the receiver operating curve (AUC). The AUC is a threshold-

independent measure that tests whether models are more likely than chance to assign higher scores to

positive outcomes, where AUC > 0.5 indicates better predictive ability than chance (Fielding & Bell

1997). I calculated AUC and corresponding 95% confidence intervals using the ci.auc function in R's

pROC package (Robin et al. 2011).

3.3.9 Comparison with observed distribution

The third aim of this chapter was to infer potential upward spread on Banks Peninsula for the target

species. Seedling establishment, growth and mortality models were extrapolated to various elevations

and compared with predictions at current distribution limits. This was only possible where elevation,

or a highly correlated variable (e.g. frost days) was a significant predictor, and assumptions are

detailed in the following paragraph. Species distribution data were collected for Banks Peninsula

through online databases, herbaria, publications and surveys (Table B.1, Figure B.1 and Figure B.2).

Where possible, relative growth, mortality and seedling establishment were predicted at the following

elevations: the 95th percentile of the observed distribution on Banks Peninsula, the maximum observed

elevation on Banks Peninsula, and at 100, 200 and 300 metres above the maximum elevation. This

allowed comparison of predicted values between ostensibly suitable elevations and beyond current

50

limits. Results were used to infer the likelihood that the species are near their elevation limits on

Banks Peninsula, or whether upward spread might occur. Comparisons between vital rates suggest

whether seedling establishment, mortality or growth will most likely determine upward spread. I

calculated 95% confidence intervals around GLMM predictions using the bootMer function in lme4,

and for GLMs of summer mortality with the predict function in base R. Some assumptions were

necessary to extrapolate models containing variables other than elevation. I assumed that observed

linear relationships between site elevation, frost and GDD variables would hold when generalizing

across the Peninsula. Post-hoc examination revealed strong linear correlations between elevation and

temperature variables, weakly positive linear correlations solar radiation, and no significant correlation

with annual precipitation (Figure B.5). Canopy cover was set to zero for extrapolations, representing

unshaded sites. Where canopy volume was a driving variable, it was set to 1 L to represent vital rates

for a small but established plant. Precipitation was set to a constant 733 mm p.a., the lower quartile of

site values (i.e. models predict elevation limits under dry, favourable site conditions). Random effects

were set to zero to give generalized predictions under mean site and source effects. The exception was

seedling establishment as it was strongly influenced by random site effects, so predictions were

generated with site effects at zero, and also with the maximum site value representing favourable sites.

Relative growth models were run for both the first year (“rapid” growth phase) and without a year

effect (“steady” growth applicable to mature plants).

3.3.10 Sources of uncertainty

While the experimental design had high power and care was taken to minimize bias, there are some

key uncertainties to note. Firstly, seedling establishment was measured out of a possible 100 seeds

sown, but seeds were planted by weight and error around this estimate is likely. In addition, seeds may

have been lost from germination trays throughout the course of the experiment, despite efforts to

prevent this. Standard potting mix eliminated site soil effects, but results may translate poorly to

responses on bare substrate. Model predictions are particularly uncertain, as in addition to the

assumptions described previously they do not account for microclimates. All models are based on two

years of data, assuming that these years are representative of longer-term climatic trends at sites, and

extreme weather events can also affect species’ range limits (Parmesan et al. 2000). Rainfall data is

particularly uncertain due to the low number of available stations and large elevation differences

between some stations and field sites (Table D.1). Orographic effects on rainfall are possible, though

elevation and precipitaiton were not highly correlated (Figure B.5). It is also debateable whether two

years is sufficient to understand processes in perennial plants (Van Der Veken et al. 2007). Despite

these uncertainties, the models provide a necessary guideline on the species’ potential to spread

beyond their current limits.

51

3.4 Results

3.4.1 Seedling establishment

Seedling emergence began between September and November 2011, and seedling counts declined

over time due to mortality and decreasing emergence. Emergence and survival was highest at low to

medium elevations, below 400 MASL (Figure 3.2a-c). Emergence was low overall; the maximum rate

observed was 35% for A. arboreum, 25% for A. haworthii and 15% for C. orbiculata. Mean viability

across all sites, however, was high (83%, 66% and 80% for A. arboreum, A. haworthii and

C. orbiculata respectively) with over half of all seeds classed as “high vigour” (Table B.3). Viability

between source sites varied by 17% for A. arboreum, 53% for A. haworthii and 44% for C. orbiculata.

Seed source random effects had a minimal impact on models (Figure 3.3a-c), with variances of 0.14

for A. arboreum, 0.38 for A. haworthii and 0.02 for C. orbiculata.

Establishment of A. haworthii correlated negatively with elevation (Figure 3.3b), and with the

exception of a single site, no seedlings survived above 319 MASL (Figure 3.3e). Aeonium arboreum

establishment was correlated negatively with annual frost days, with lesser effects of annual

precipitation (-) and GDD5 (+), resulting in a similar response to elevation as A. haworthii (Figure

3.3d). No A. arboreum seedlings established above 358 MASL; while up to 17% emerged at higher

sites, none survived. Cotyledon orbiculata differed from Aeonium species as neither elevation nor

temperature correlated with establishment. Annual precipitation was the only significant variable, with

higher establishment at dry sites (Figure 3.3f). However, no seedlings survived above 370 MASL.

Final models of seedling establishment were significantly better than null models according to Chi-

squared tests (p < 0.001). Marginal R2 values were higher for Aeonium species (A. arboreum 0.76,

A. haworthii 0.47) than C. orbiculata (R2 of 0.35), and conditional R

2 show additional unexplained

variation within random effects (A. arboreum 0.85, A. haworthii 0.76 and C. orbiculata 0.80). Models

of all three species predicted binary outcomes well (seedlings establish yes/no), as AUC values were

high (0.95 ± 0.01 for both Aeonium species, 0.91 ± 0.01 for C. orbiculata).

3.4.2 Annual relative growth

Annual relative growth differed markedly between years. Rapid initial growth was followed by

levelling off, or some die back, over the remainder of the experiment (Figure 3.4). Aeonium species

grew larger than C. orbiculata; in November 2012, the mean A. arboreum was 13.5 L ± 1.1 (SE) in

volume, A. haworthii was 7.5 ± 0.9 L, and C. orbiculata 3.2 ± 0.3 L. This is despite Aeonium plants

having a lower mean initial volume than C. orbiculata (0.1 ± 0.006 L, 0.05 ± 0.002 L, and

0.2 ± 0.01 L for A. arboreum, A. haworthii, and C. orbiculata). Relative growth also varied with

elevation. When divided into bins of low (0 - 150 MASL), medium (150 - 400 MASL), and high

(400 - 700 MASL) elevations, plants at high elevations exhibited fluctuating periods of dieback and

recovery, and the lowest net relative growth at the end of the experiment (Figure 3.4).

52

Figure 3.2 Mean seedling count at measurement intervals with 95% confidence intervals, for

a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata. Sites are divided into low (0 – 150

MASL), medium (150 – 400 MASL), and high (400 – 700 MASL) elevations. Seedling models are

based on November 2012 counts.

53

(a) (b)

(c) (d)

(e) (f)

Figure 3.3 Coefficients of GLMMs of probability of probability of seedling establishment (P[SEst]) ±

95% confidence intervals, with fixed (solid) and random (hollow) effects, for a) Aeonium arboreum c)

A. haworthii and e) Cotyledon orbiculata, and GLMM predictions (lines) and raw data (points) for b)

A. arboreum, d) A. haworthii and f) C. orbiculata. Predictions use fixed only effects between 0 – 1000

MASL (b, d), and 400 – 1400 mm p.a. (f). For A. arboreum (b), constant precipitation of 733 mm p.a.,

and linear relationships of GDD5 and frost days to elevation are assumed (section 3.3.9). Thus, lines

are not fitted to points.

54

Figure 3.4 Mean relative growth, as [ln(Volumet+1)- ln(Volumet)], since November 2010 baseline volumes at low, medium, and high elevations for a) Aeonium

arboreum, b) A. haworthii, and c) Cotyledon orbiculata. Here, t is measured in units of half-years. Shaded area shows 95% confidence interval of the mean.

55

(a) (b)

(c) (d)

(e) (f)

Figure 3.5 GLMM coefficients ± 95% confidence intervals of annual relative growth (RG) models,

calculated as [ln(Volumet+1)- ln(Volumet)], with fixed (solid) and random (hollow) effects, for a)

Aeonium arboreum, c) A. haworthii and e) Cotyledon orbiculata. GLMM predictions (lines) and site

means with standard errors (points) in years one and two, shown for b) A. arboreum, d) A. haworthii

and f) C. orbiculata. Predictions generated using only fixed effects between 0 – 1 000 MASL. A linear

relationship of annual frost days with elevation is assumed (section 3.3.9). Canopy cover (CC) is set to

zero for C. orbiculata. Thus, lines are not fitted to points.

56

The key variables in growth models of all three species were elevation (as a quadratic term) and

annual frost days, with both of which growth was negatively correlated (Figure 3.5a-c). Relative

growth was highest at around 200 MASL for A. arboreum and C. orbiculata, and sea level for

A. haworthii (Figure 3.5d-f). Canopy cover was also a good predictor for C. orbiculata, where open

plots were more favourable. Fixed year effects show that for all three species, growth in year one was

considerably higher than in year two. Site remained an important source of variation in all three

models (variance 0.45, 0.79, and 0.45, for A. arboreum, A. haworthii, and C. orbiculata) relative to

plant source (variance 0.01, 0.00, and 0.04 respectively). Final models of relative growth performed

significantly better than null models for all species (p < 0.001). Marginal and conditional R2 values

indicated high levels of explanatory power from fixed effects relative to random effects: 0.71 vs. 0.78

for A. arboreum respectively, 0.65 vs. 0.74 for A. haworthii, and 0.54 vs. 0.66 for C. orbiculata.

3.4.3 Mortality

Mortality was highly seasonal and showed a clear positive relationship with elevation. There were

fewer deaths over the December - May “summer” period than the June-November “winter” period

(final mortality in summer vs. winter: 2% vs. 17% for A. arboreum, 5% vs. 27% for A. haworthii, and

3% vs. 16% for C. orbiculata). In general, mortality increased with elevation regardless of season

(Figure 3.6a-c). Above 400 MASL, 87% of A. arboreum individuals were dead after 2 years, 97% of

A. haworthii, and 69% of C. orbiculata. Mortality also increased over time. There were more deaths in

year two than year one, where mortality rose by 17% for A. arboreum in the second year, 13% for

A. haworthii and 27% for C. orbiculata. This appeared to be due to increasing plant damage over time.

Plants that died over summer tended to be smaller than survivors (Figure B.6a-c). There was a

negative relationship between canopy volume and summer mortality in all three species (Figure 3.6),

and canopy volume was the strongest explanatory variable in the models. Elevation significantly

improved models of summer mortality for Aeonium species. Intercept terms were negative indicating

low probability of death for plants with a mean canopy volume. Final models of mortality performed

better for A. arboreum and A. haworthii than for C. orbiculata (Pseudo-R2 = 0.41, 0.55 and 0.19

respectively), but all constitute excellent fit (McFadden 1973). Model AUCs indicate excellent

prediction for both Aeonium species (0.95 ± 0.04 for A. arboreum and 0.96 ± 0.04 for A. haworthii),

and good prediction for C. orbiculata (0.73 ± 0.18).

Canopy volume, time, and frost days explained variation in winter mortality for all three species.

Individuals that died were smaller on average than survivors (Figure B.6a-c), meanwhile mortality

increased in the second winter and with increasing number of frost days. To reflect repeated cold

stress over time, cumulative frost days were used in GLMMs instead of a fixed year effect, as it was

more biologically meaningful and significantly improved model fit. Because of the non-normal

distribution of cumulative frost days, this variable also needed to be log-standardized in the same way

as canopy volume (equation 3). Cumulative frost was used in winter mortality models only, as

57

mortality was the only vital rate that showed such change over time (although relative growth also

changed over time, this is explicable with ontogenetic drift). Models show that large plants withstood

fluctuating dieback and recovery, but small plants were only able to survive given favourable

conditions (Figure B.6d-f). Frost was the most important predictor of winter mortality regardless of

plant size (Figure 3.7a-c.), but only large plants are predicted to survive harsh conditions (Figure B.7a-

c). Fixed effects explained most of the among site variation in winter mortality, with the exception of

C. orbiculata (marginal vs. conditional R2 of final models were 0.84 vs. 0.86 for A. arboreum, 0.74 vs.

0.85 for A. haworthii, and 0.53 vs. 0.95 for C. orbiculata). Model AUCs showed good prediction of

binary outcomes (A. arboreum and A. haworthii 0.96 ± 0.02, C. orbiculata 0.97 ± 0.02).

3.4.4 Elevation limits on Banks Peninsula

Currently, A. arboreum has the lowest distribution limit on the Peninsula (maximum 177 MASL), and

C. orbiculata the highest (maximum 381 MASL). For both Aeonium species, the greatest difference

between predictions at current elevation limits and 100 m higher was in winter mortality (Table 3.3).

Even at A. haworthii's current limits, predicted winter mortality is high and seedling establishment is

low. Just 100 m higher, and winter mortality is predicted to be 88%, and seedling establishment < 1%.

Predictions for A. arboreum, meanwhile, are more favourable at its current limits, but a 100 – 200 m

rise leads to similar predictions of growth, mortality and seedling establishment to A. haworthii at its

distribution limit. Only two of the four vital rates modelled were correlated with elevation or

temperature for C. orbiculata. Of those, relative growth declined most sharply as elevation increased,

with net growth (the sum of both predicted RGs) becoming negative 200 m above its current

distribution. However, winter mortality, based on a 1 L canopy volume, does not reach 75% (predicted

mortality at A. haworthii's current maximum elevation) until 681 MASL. It is unclear whether relative

growth will be sufficiently limiting to C. orbiculata to prevent establishment of plants 1 L or more in

volume that could survive multiple winters.

Prediction intervals were generally narrow, with the notable exception of winter mortality for

A. haworthii and C. orbiculata. This indicates a high degree of confidence overall, but that winter

mortality models should be interpreted with some caution. Random effects were not included in model

predictions with the exception of seedling establishment, where predictions were also generated using

the maximum site values. This was because site remained an important source of variation in seedling

models, and heavily influenced model predictions. Under the assumption that site represented

unknown environmental conditions, the maximum site intercept was used to predict seedling

establishment at high elevations with all other environmental factors being favourable.

58

(a) (b)

(c) (d)

(e) (f)

Figure 3.6 Coefficients of binomial GLMs of summer mortality with 95% confidence intervals, for

a) Aeonium arboreum, c) A. haworthii and e) Cotyledon orbiculata, and percentage of surviving

individuals at each measurement period, at low, medium, and high elevations for b) A. arboreum,

d) A. haworthii and e) C. orbiculata. Percentages measured out of n = 50 individuals at low and high

elevations, and n = 100 at medium elevations.

59

(a) (b)

(c) (d)

(e) (f)

Figure 3.7 Logistic GLMM coefficients of winter mortality ± 95% confidence intervals, with fixed

(solid) and random (hollow) effects, for a) Aeonium arboreum, c) A. haworthii and e) Cotyledon

orbiculata, and modelled probability of death (P[Die], lines) and observed mortality per site (points)

vs. elevation, for b) A. arboreum, d) A. haworthii and f) C. orbiculata. Predictions (lines) generated

for small (0.125 L), medium (1 L), and large (8 L) plants, using only fixed effects between 0 – 1000

MASL. A linear relationship of annual frost days with elevation is assumed, derived from recorded

data. Consequently, lines are not fitted to points.

60

Table 3.3 Modelled seedling establishment (SEst), relative growth (RG) and summer and winter mortality (SM and WM), at various elevations (MASL), for

Aeonium arboreum, A. haworthii and Cotyledon orbiculata. No random effects included except for SEst max, predicted seed establishment at the most favourable

site using the highest random site effect. Predictions given for the 95th percentile of the observed distribution (+), the maximum observed elevation (*, bold), and up

to 300 MASL above the observed limit. The 95% prediction intervals are denoted by ±. Frost and GDD assumed to increase linearly with elevation, other variables

set to constant values.

A. arboreum A. haworthii C. orbiculata

MASL SEst SEst max RG Y1 RG SM WM MASL SEst SEst max RG Y1 RG SM WM MASL RG Y1 RG WM

+152 ± 0.004

± 0.004

± 0.060

± 0.004

± 4.79

± 0.35

± 0.34

± 0.36

± 0.01

± 0.04

± 0.23

± 0.17

*177 ±0.003

± 0.003

± 0.040

± 0.003

± 4.80

± 0.37

± 0.35

± 0.39

± 0.01

± 0.04

± 0.31

± 0.19

+160 ± 0.003

± 0.004

± 0.060

± 0.004

± 4.58

± 0.51

± 0.74

± 0.53

± 0.01

± 0.03

± 0.30

± 0.23

277 ± 0.001

± 0.001

± 0.010

± 0.001

± 4.61

± 0.46

± 0.15

± 0.45

± 0.01

± 0.05

± 0.61

± 0.14

*303 ± 6 × 10-4

± 9 × 10-4

± 0.010

± 9 × 10-4

± 3.89

± 0.64

± 0.05

± 0.67

± 0.03

± 0.05

± 0.75

± 0.23

+252 ± 2.75

± 0.41

± 0.15

± 0.42

± 0.01

± 0.44

377 ± 2 × 10-4

± 5 × 10-4

± 0.003

± 5 × 10-4

± 4.06

± 0.45

- 0.39

± 0.45

± 0.03

± 0.05

± 0.79

± 0.10

403 ± 2 × 10-4

± 4 × 10-4

±0.003

± 4 × 10-4

± 3.13

± 0.66

- 0.70

± 0.71

± 0.06

± 0.07

± 0.88

± 0.29

*381 ± 2.39

± 0.42

- 0.21

± 0.45

± 0.13

± 0.46

477 ± 6 × 10-5

± 3 × 10-4

± 0.001

± 3 × 10-4

± 3.16

± 0.42

- 1.30

± 0.45

± 0.05

± 0.06

± 0.88

± 0.07

503 ± 5 × 10-5

± 2 × 10-4

±0.001

± 2 × 10-4

± 2.14

± 0.73

- 1.69

± 0.77

± 0.13

± 0.13

± 0.94

± 0.33

481 ± 1.92

± 0.39

- 0.69

± 0.40

± 0.34

± 0.47

603 ± 2 × 10-5

± 7 × 10-5

± 3 × 10-4

± 7 × 10-5

± 0.93

± 1.02

- 2.90

± 1.11

± 0.27

± 0.25

± 0.96

± 0.35

581 ± 1.26

± 0.48

- 1.34

± 0.54

± 0.57

± 0.49

681 ± 0.42

± 0.85

- 2.18

± 0.91

± 0.75

± 0.49

61

3.5 Discussion

There is strong evidence that the distributions of A. arboreum, A. haworthii and C. orbiculata on

Banks Peninsula are limited by climate, with a plant performance declining with increasing elevation.

This is consistent with the fact that New Zealand marks the coldest and wettest extremes of the

species’ realized niches and therefore, they are likely to be close to their limits of cold tolerance (see

Chapter 2). In the Aeonium species, performance declined with increasing elevation and its covariates

across all vital rates measured (seedling establishment, relative growth, summer and winter mortality).

In C. orbiculata, only relative growth and winter mortality were associated with elevation or its

correlates. The provenance of cuttings and seeds had a negligible effect on plant performance and

germination, as demonstrated by the consistently negligible effect of the random source effect in

GLMMs, and there is consequently no evidence for an adapted fitness gradient across Banks Peninsula

[e.g. Holt and Keitt (2005)].

3.5.1 Predicted limits

Model extrapolations within and above the species’ current distributions on the Peninsula suggest that

all three are close to their elevation limits in the region. Aeonium haworthii appears to be closest to its

limits, with 75% winter mortality and less than 1% seedling establishment predicted at its current

maximum elevation. It appears unlikely that survival and seedling establishment of A. haworthii

would be sufficient to facilitate colonization at much higher elevations. Models predict that

A. arboreum would reach similar seedling establishment, growth and mortality rates at around 100 –

200 m above its current range. Assuming that A. haworthii’s vital rates are close to limiting at its

current range edge, both Aeonium species are likely to have similar maximum elevations (around 300

MASL). Cotyledon orbiculata, meanwhile, is currently found at elevations where steady relative

growth is predicted to be negative (381 MASL). However, at these elevations the rapid growth phase

(year one) is strongly positive, so although plants at these elevations should be smaller than their low-

elevation counterparts, they might still persist over a number of years. It is possible that similar

populations of small plants could establish and survive well beyond the current limits, subject to

relative growth. Again taking A. haworthii’s predicted rates at current limits as a reference, a 1 L

C. orbiculata plant is not predicted to experience comparable winter mortality until 300 m above its

current maximum (681 MASL).

All three species appear to be restricted to lower elevations in New Zealand than in their native ranges.

In the case of the two Aeonium species this may be primarily explained by the difference in latitude

between the native and New Zealand ranges. Using Hopkins’ Bioclimatic Law (1920) as a rough

estimate, the equivalent elevation of 400 MASL in New Zealand (slightly above the maximum

elevation of A. haworthii in New Zealand, according to distribution data), would be approximately

2300 MASL in Tenerife when adjusted for latitude. Similarly, the maximum elevation of A. arboreum

in Morocco of 1600 MASL would equate to roughly sea level in New Zealand. While these are not

62

highly accurate calculations, they illustrate that elevation is not necessarily comparable between the

ranges. However, the dramatic differences in limits of C. orbiculata between ranges cannot be

explained by latitude alone, as the highest elevation occurrences in the native range, Lesotho, are

climatically very similar to Central Otago in New Zealand (according to the “match climates” function

in CLIMEX™), where the minimum temperatures are much lower than anywhere on Banks Peninsula.

A possible explanation for this is that frost tolerance in regional populations of C. orbiculata differ

strongly across the native range, and these traits are heritable (Van Coller & Stock 1994). The cold

limitation documented in this study suggests that the C. orbiculata in New Zealand are more likely to

have originated from less-hardy, low-elevation populations in South Africa than hardy high-elevation

populations, e.g. in Lesotho.

Results also indicate that the three species’ vital rates are not equally limiting to upward spread. There

is considerable similarity in predictions of seedling establishment, relative growth and mortality

between both Aeonium species. Of these, winter mortality appears to be the key limiting factor for

upward spread, followed by seedling establishment, while summer mortality and relative growth in the

rapid phase do not appear to be limiting. Conversely, C. orbiculata appears to be restricted primarily

by relative growth. Elevation is a poor predictor of seedling establishment for C. orbiculata on Banks

Peninsula, and while winter mortality increases with elevation, summer mortality is only indirectly

linked to climate through canopy volume.

3.5.2 Climatic drivers

Although climatic predictors differed between models of vital rates, there was similarity between

species in key driving variables and responses. This is consistent with the fact that, while the species’

native ranges differ, they have adopted similar life strategies. These include CAM photosynthesis,

drought tolerance and occupancy of bare habitats (Webb et al. 1988; Vogan 2003). Surprisingly,

precipitation was rarely a good predictor of plant performance, most probably because there were few

weather stations available, but potentially the precipitation gradient across Banks Peninsula might not

be sufficiently limiting.

Climatic predictors were markedly different between vital rates, indicating a variety of pressures

acting across life stages. Comparable patterns have been found in a number of other species,

e.g. Lacuta serriola L. (Prince & Carter 1985) and Impatiens glandulifera Royle. and Heracleum

mantegazzianum Sommier & Levier. (Willis & Hulme 2002), and is to be expected. The key correlate

of relative growth in all species was a quadratic relationship with elevation, where growth peaked

between sea level and 200 MASL. This could perhaps be a result of higher light competition at low

sites and harsher climatic conditions at high elevations, but it is difficult to infer whether it is limiting

as reduced growth under stress may be beneficial for energy conservation (Grime & Hunt 1975).

Mortality was partially dependent on canopy volume in all species, whereby smaller plants had a

lower probability of survival in both winter and summer. This could simply be an effect of age-

63

specific mortality (Michod 1979), and given more years of observations mortality in large plants might

rise as they approach their life expectancy. Alternatively, it may reflect that smaller plants are less

tolerant of die back associated with harsh climatic conditions. The cumulative frost term in winter

mortality models means that as individuals accumulate frost damage over time, they must recover and

grow in order to avoid increasingly severe damage and eventually, death. The only models which

differed strongly between species were seedling establishment. Seedling establishment in A. arboreum

was largely correlated with frost (-) and GDD5 (+), which overall leads to similar responses as the

elevation-based model for A. haworthii, although precipitation (-) was also significant for A. arboreum

and does not correlate well with elevation. Generally, temperature appears to be important for the

germination and seedling survival of Aeonium species across the Banks Peninsula, and A. arboreum

additionally requires relatively dry conditions. In contrast, the only predictor of C. orbiculata seedling

establishment was precipitation, as a negative effect.

The most common climatic predictors across all models were frost days and elevation. Frost often

limits species’ distributions (Larcher 2005) and this is consistent with the species’ traits; succulents

have a high water content and should therefore be sensitive to freezing damage (Nobel 1981; Luttge

2004). Yet, freezing avoidance has been documented in some succulents (Stuckey & Curtis 1938; Loik

& Nobel 1993) and reported fatal temperatures of the study species in their native ranges are much

lower than those encountered during this field experiment (Lösch & Kappen 1981; Van Coller &

Stock 1994). This apparent contradiction potentially highlights the difficulties in reconciling

laboratory results with responses in the field. The effect of elevation, meanwhile, is less easy to

interpret biologically, as climatic and non-climatic factors correlate with this variable (Körner 2007;

Pauchard et al. 2009). Many of these confounding effects were accounted for in the experimental

design: for example, soil was a standard mix, and sites were secured to ensure minimal disturbance or

grazing, and plots were weeded to minimize competition. It follows, then, that the response to

elevation is likely due to climatic effects. Aside from temperature, other variables which often change

with elevation include decreasing pressure with increased elevation, and higher solar and UVB

radiation under clear skies (Körner 2007). However, modelled solar radiation was a poor predictor in

all cases, and there is arguably not an extreme enough elevation gradient for atmospheric conditions to

be limiting. Seasonality has a complex relationship with elevation (Körner 2007) and while seasonal

effects are possible, high elevation negatively affected all species despite differences in their growing

seasons (Aeonium species in winter, C. orbiculata in summer). It is most plausible that the relationship

with elevation is a proxy for increased snow cover, as severe damage and mortality were commonly

observed at sites immediately following heavy snowfall. Although snow can have protective

properties as a thermal insulator, prolonged snow cover can limit respiration, cause anoxia, impair root

activity through ground ice, encourage mould and stunt growth (Körner 2003). Unfortunately there are

no regional snow data, although testing plant responses against modelled data might assist in

disentangling the importance of elevation for the species.

64

Cotyledon orbiculata was the only species that responded to canopy cover, exhibiting low relative

growth and winter survival under increasing cover. A likely mechanism is the photoprotective

epicuticular wax of C. orbiculata, which both Aeonium species lack. While the thickness of the wax

varies in response to light conditions, it is detrimental to performance in low light (Barker et al. 1997).

It is likely that invasion of C. orbiculata will be limited to more open environments and largely absent

from areas under dense canopy.

3.5.3 Implications for Banks Peninsula

Results indicate that A. arboreum and A. haworthii are currently near or at their climatic limits on

Banks Peninsula. While upward spread is likely to be minimal, continued colonization of coastal

headlands and bays (infilling) in the region appears likely, subject to habitat availability and dispersal

patterns. As such, the threat from the two Aeonium species to high elevation rock outcrops, where the

majority of the regions’ endemic species are found (Wiser & Buxton 2009), is low. The interpretation

for C. orbiculata is more nuanced, as persistence at high elevations will depend on whether plants are

able to reach sufficient size to survive and recover from winter frosts. It is unknown whether

C. orbiculata would be able to complete its life cycle above its current maximum elevation, and

although arguably unlikely, marginal populations cannot be discounted. This, in conjunction with the

wider range of habitats it is capable of colonizing (Figure A.3, Figure A.7), suggests that C. orbiculata

poses a greater threat to the region than either Aeonium species.

Non-climatic factors that vary with increasing elevation were not accounted for in model predictions.

Dispersal barriers and pollinator availability are presumed not to be limiting at the scale of Banks

Peninsula as the species produce “dust-like” seeds (van Rheede van Oudtshoorn & van Rooyen 1999)

and can self-pollinate (Zietsman 1998). Slope and disturbance increase with elevation but this is

unlikely to limit species that preferentially occupy vertical, disturbed habitats e.g. cliffs and outcrops.

Factors expected to be relevant to the species on Banks Peninsula include soil, land use, and

anthropogenic activity. As elevation increases in the region, soil pH tends to become less acidic. Soils

at low elevations are predominantly Fragic Pallic and Fluvial Recent, characterized by poor structure,

high nutrient content, low organic matter and high erosion, often with loess deposits. At higher

elevations these give way to Brown soils (Firm and Mafic) which are stable, with higher clay content

and firmer structures and topsoil (Landcare Research 2015). The species generally prefer free-draining

soil (Vogan 2003), therefore Brown soils are likely to be less suitable. However, there is no shortage

of exposed rock outcrops at high elevations in the region. There is very little difference in land use

with increasing elevation; high-production exotic grassland dominates Banks Peninsula, with a slight

increase in forested areas and scrubland at higher sites, although anthropogenic disturbance is lower

due to fewer roads and homesteads (Boffa Miskell 2007; Ministry for the Environment & Landcare

Research 2014). Fire regimes might also vary with elevation as a result of vegetation and soil drainage

changes, and though the related Bryophyllum delagoense (Ecklon & Zeyher) is likely facilitated by

fire in Australia (Witt & Nongogo 2011), the target species’ responses to fire are unknown and there

65

are no fine-scale fire data for Banks Peninsula. It seems probable that the non-climatic covariates of

elevation will have minimal effects on the upward spread of A. arboreum, A. haworthii or

C. orbiculata on Banks Peninsula, and that their eventual distributions will be largely determined by

climate and propagule pressure.

3.5.4 Limitations

This study goes into greater detail than many transplant studies, which often investigate a single vital

rate [e.g. Paiaro et al. (2007)], do not extrapolate beyond the current distribution [e.g. Kollmann and

Bañuelos (2004)], or do not standardize for effects of source population (Hargreaves et al. 2014).

Nevertheless, there are limitations to be considered when interpreting the results. The implications of

model uncertainty are most severe for seedling establishment, as the three species produce vast

numbers of seeds; varieties of C. orbiculata are reported to produce over 1000 viable seeds per flower

in the native range, and flowers are numerous (Zietsman 1998). Even if a small percentage of seeds

germinate and survive, it is still plausible that populations could establish, and variation in germination

could have a large effect on population growth rate. Additionally, predictions assume linear

correlations with frost and GDD5, while other factors were set to constant values (e.g. precipitation

and canopy cover). Running A. arboreum seedling models under high precipitation (1100 mm p.a.)

reduced predicted establishment at 177 MASL by 83%. A similar effect occurs with canopy cover for

C. orbiculata models. It is therefore impossible to define absolute elevation limits, and estimates

reflect cautious predictions assuming otherwise optimal (i.e. dry, open) conditions. Furthermore, as

plants did not flower during the experiment in sufficient numbers, reproductive output could not be

tested. Fecundity may also be limiting to population persistence, and knowledge of seed output would

allow classification of source and sink populations.

3.5.5 Conclusions

The aims of this study were to investigate whether A. arboreum, A. haworthii and C. orbiculata are

close to their climatic limits on Banks Peninsula and to assess the potential for upward spread. There is

evidence that climate is strongly limiting to plant performance across the region, and that Banks

Peninsula represents a gradient from favourable climates to those beyond the species’ cold tolerances.

Aeonium populations have reached almost their maximum elevation, which is likely to be around

300 MASL. Interpretations for C. orbiculata are less certain and it is possible that populations could

persist beyond their current maximum elevation. Winter mortality, relative growth and seedling

establishment of Aeonium species are all limiting at high elevations, while only relative growth

appears to be limiting for C. orbiculata. Because C. orbiculata is less restricted by habitat type and

climate than the Aeonium species, it evidently poses the highest risk to Banks Peninsula of the three

species.

66

Chapter 4 – Exploring the link between fecundity and climate in

naturalized populations of alien Crassulaceae

4.1 Abstract

Fecundity is an important facet of plant invasions. It shapes range limits and determines whether

populations can self-sustain, and sometimes favours non-native species over native or other introduced

competitors. In turn, fecundity is usually affected by climate. Climate acts directly e.g. through floral

vernalisation, or indirectly e.g. through growth rates or biotic interactions. Here, I examine fecundity

in three succulent plants naturalized in New Zealand: Aeonium arboreum, A. haworthii and Cotyledon

orbiculata. Knowledge is scarce regarding the species’ reproductive rates or how climate affects them,

and this is the first study to measure the species’ fecundity in the introduced range. In this chapter, I

investigate the climate-fecundity relationship in A. arboreum, A. haworthii and C. orbiculata across

their current ranges on Banks Peninsula, a region that is a New Zealand hotspot for all three species. I

surveyed rates of flowering, as well as inflorescences per plant, flowers per inflorescence and seeds

per pod, in eight naturalized populations per species across a gradient of climatic conditions.

Reproductive traits were modelled against climatic variables as well as maternal plant size to test for

direct and indirect climatic effects. Direct effects of climate were only found in A. arboreum and

C. orbiculata, predicting higher probability of flowering with increasing heat sum and solar radiation,

respectively. The majority of variation in A. haworthii was not explained, and aspect was the only

environmental predictor of inflorescences, flowers or seeds in any species. Potential indirect effects of

climate were found in all species, as plant size was a predictor of at least one reproductive trait per

species. Total seed output was highest for C. orbiculata, the most prolific invader of the three,

producing approximately 190 000 seeds per capita on average. I found no evidence that climate is

limiting to fecundity in any of the three species within the gradient studied, as direct effects were weak

and the size-fecundity relationship was ambiguous. All three species produced numerous seeds, and

small populations may still constitute considerable seed sources within the majority of climatic

conditions currently occupied on Banks Peninsula.

Keywords: Crassulaceae, fecundity, climate, survey, invasions

4.2 Introduction

Reproductive traits are key determinants of distributions, abundance, and population dynamics in

higher plant species (Howe & Smallwood 1982). The fecundity of non-native species is commonly

used to forecast risk and range limits in invaded ranges (Willis & Hulme 2002; Walter et al. 2015), to

investigate establishment success after introduction (Thompson et al. 2001; Pyšek et al. 2009;

McGregor et al. 2012) and to inform pest management (Parker 2000; Wadsworth et al. 2000). The

number of viable seeds produced by an individual fundamentally limits its number of offspring, while

67

on a larger scale, spatial patterns are often explained by dispersal (Harper 1977). Seed production and

dispersal is, in turn, regulated by climate. Climatic constraints shape all species’ distributions

(Woodward 1987), where populations at range edges are sometimes sink populations, incapable of

self-sustaining without immigration from nearby seed sources (Hargreaves et al. 2014). Any species’

potential distribution therefore depends on the relationship of fecundity to climate. By ignoring this

relationship, we may confound sink populations with suitable conditions, and in the context of

invasions over-estimate future spread. Conversely, if no decline in fecundity or sink populations are

present, it may be that the species is yet to reach climatic equilibrium in the invaded range (Hargreaves

et al. 2014).

While total propagule pressure is a major determinant of spread of non-native species (Holle &

Simberloff 2005; Lockwood et al. 2005), climate can inhibit or facilitate fecundity at many points on

the continuum from flowering to seed dispersal. Climate can affect each stage differentially, and can

influence fecundity either directly or indirectly. Direct climatic limitations include vernalisation or

floral initiation through temperature (Taiz & Zeiger 1991), meeting temperature requirements for

embryo development and seed maturation (Walck et al. 2011), or specific conditions for breaking seed

dormancy, e.g. chilling (Baskin & Baskin 1998). Indirectly, climate can influence flowering by

altering overall plant performance, resource allocation, and plant size, which is often a predictor of

fecundity (Harper & White 1974; Herrera 1991). In addition, pollinators and dispersal agents may vary

in abundance or behaviour according to climatic conditions (Hegland et al. 2009). In the absence of

pollinators, many species are auto- or geitonogamous, but selfing can lower progeny fitness (Munguía-

Rosas et al. 2013; Wright et al. 2013) and seed output (Zietsman 1998). As such, when identifying

climatic constraints on fecundity it is useful to break reproduction down into discrete stages:

probability of flowering, number or size of flowers, number and viability of seeds, etc. Doing so may

reveal patterns and limitations otherwise masked by estimates of overall fecundity (Herrera 1991).

Variation in fecundity can be pivotal to invasion success, determining where and how rapidly different

species spread, and their interactions with native competitors. Phenological differences are a predictor

of invasion success in a number of species, where prolonged flowering offers an advantage over

natives or other invaders (Goodwin et al. 1999; Cadotte & Lovett-Doust 2001; Lloret et al. 2005). In

some non-native species, high nectar yields and bright floral blooms may offer an advantage by

attracting pollinators, thus increasing seed yield (Ghazoul 2002). This is exacerbated when non-native,

“showy” plants are preferentially planted as ornamentals over native species (Li et al. 2004). At the

dispersal stage, traits of non-native species sometimes favour regeneration success, longer dispersal

distances or attractiveness to foragers (Westcott & Fletcher 2011). It is not only relative to natives that

non-native plants can have reproductive advantages; some species exhibit elevated fitness in the

invaded range relative to their own native ranges, often attributed to release from natural enemies

(Keane & Crawley 2002), and facilitating spread to novel environments (Edwards et al. 1998; Jakobs

et al. 2004). It is therefore valuable to measure species’ fecundity in the introduced range as it may

68

differ to the native range, and because invasion success is tied closely to reproductive output. Single

measures of fecundity can assist in understanding the success of invasive species relative to other

species, but by extending these measures along climate gradients encompassed by the species’

distributions, we gain additional insight into their potential distributions.

In previous chapters, I examined the potential distributions of Aeonium arboreum, A. haworthii and

Cotyledon orbiculata in New Zealand, and using a field experiment measured mortality, growth and

germination along a climatic gradient on Banks Peninsula. For a complete understanding of the

species’ climatic limits on Banks Peninsula, it was important to test whether fecundity varies with, or

is limited by, climate. For ethical and legal reasons the species were prevented from reproducing

during the field experiment, so fecundity data were collected from wild populations. By measuring

flowering and seed production along the climate gradient of the species’ current distributions, I aimed

to infer whether climate currently limits their reproduction and whether more widespread species have

higher seed output. Fecundity may be particularly important to the invasion of these three species;

their popularity as ornamentals is partly due to their large, colourful inflorescences, and non-native

ornamentals may have a particularly strong advantage in New Zealand as the native flora are

predominantly white-flowered, are not specialized, and are not “showy” (Lee et al. 2001). Propagule

pressure from naturalized populations is also potentially high, as their numerous, wind-dispersed seeds

could potentially travel long distances (van Rheede van Oudtshoorn & van Rooyen 1999). It was

envisaged that this study would inform risk forecasting and future management of the target species.

4.2.1 Aims

1. To determine whether reproductive traits (probability of flowering, inflorescences per plant,

flowers per inflorescence, and seeds per pod) of Aeonium arboreum, A. haworthii and

Cotyledon orbiculata vary predictably along the climatic gradient encompassed by their

current distribution on Banks Peninsula, and hence whether climatic constraints on fecundity

might limit their current or potential distributions.

2. To determine which reproductive stages, and which climatic or non-climatic variables, most

affect per capita seed production across Banks Peninsula.

3. To compare overall seed output per capita between species, under the hypothesis that less

widespread species would produce fewer seeds.

4.3 Methods

4.3.1 Study species

As in previous chapters, I focussed on Aeonium arboreum, A. haworthii and C. orbiculata. Fecundity

data for the three species are sparse, with no information for New Zealand except for the fact that they

flower and produce viable seed readily (Webb et al. 1988). In their native ranges, Aeonium species

69

flower in spring or summer (Levin 2006), while C. orbiculata flowers in the dry season (Eller &

Ferrari 1997). Pollination is thought to occur via wind, water droplets and generalist insects in the case

of Aeonium species (Alamo et al. 1996), and sunbirds in the case of C. orbiculata (Zietsman 1998).

All three species are also capable of self-pollination. The resulting seeds are wind-dispersed,

numerous, and small (van Rheede van Oudtshoorn & van Rooyen 1999). There are no studies of seed

size or output in Aeonium species, but C. o. var. dactylopsis reportedly produces an average 1500

seeds per flower in its native range when hand-pollinated, with a mean seed weight of 51 µg (Zietsman

1998). Seed survival in other Crassulaceae species is low ( < 2%) regardless of climate (Daws et al.

2007), and germination of other Aeonium species in their native range reportedly varies between 2 and

84% (Alamo et al. 1996). Low germination rates combined with the energy constraints associated with

small seeds indicates an r-selection strategy, so in the absence of barriers, seeds should be numerous.

There are no previous studies of Crassulaceae species’ fecundity in New Zealand, or their climatic

constraints, although flowering of the non-native congener A. canariense (L.) Webb & Berthel. has

been anecdotally linked to frost (Anon 1950). There is some evidence that flowering in Aeonium

species is related to plant size. Jorgensen and Olesen (2001) describe deterministic modular growth in

Aeonium species in the native range, based on the clear annual internodes of stem growth common to

all species in the genera. They provide linear formulae for the probability of flowering based on the

position of modules. However, these formulae are of limited use in New Zealand as they do not

account for climatic limitation, were calculated in the native range, and counting all internodes can

require uprooting the plant.

4.3.2 Study area

The study area for this chapter is Banks Peninsula, New Zealand, the region where field experiments

were conducted (Chapter 3). All three species are found only in the warmest, driest parts of Banks

Peninsula between 0 - 400 MASL, and mostly along the northern coastline (Figure 4.1a-c). While the

species are likely to be limited by the climate gradient of Banks Peninsula, suitable habitat (e.g. cliffs,

rock outcrops) is abundant. Furthermore, as demonstrated in Chapter 3, at least two of the species

(Aeonium species) appear to be approaching their climatic limits in the region, consequently

naturalized populations were expected to exhibit some climatic limitation near range margins. All

three species ostensibly produce sufficient seed on Banks Peninsula to colonize and form self-

sustaining populations; the region is where all three species were first described as naturalized (Healy

1959), and there are now more occurrence records on Banks Peninsula than elsewhere in New Zealand

(Chapter 2). It is useful to measure seed output in the region to assist with population control by local

authorities (Di Carter, pers. comm., 2010). Further spread is of concern due to invasion of pasture by

the toxic C. orbiculata (Botha & Penrith 2008), and colonization of the unique ecosystems of the cliffs

and outcrops by all three species (Wiser & Buxton 2009; Holdaway et al. 2012).

70

4.3.3 Flowering surveys

Permanent transects were marked within eight distinct naturalized populations per species. Based on

results of a preliminary presence-absence survey (Section C.1, Figure C.1), four main areas were

chosen for each species, representing the range of temperature and precipitation across the three

species’ regional distributions. Unfortunately, following an earthquake in February 2011, the high

elevation areas selected for A. haworthii and C. orbiculata became inaccessible. I was thus restricted

to surveying between the warmest and driest areas in Sumner, and cooler and wetter areas in the

northern and eastern bays (Figure 4.1a-c, Figure C.3). Within each of the four main areas, two survey

sites were selected. They were intended to be paired replicates, but later investigation of temperature

data revealed they were too different to be paired for analyses. Sites were chosen based on population

size (requiring at least 50 individuals per site), and accessibility (i.e. some cliff populations were

inaccessible). See Table C.1 for site descriptions. Estimated abundance and accessibility in wild

populations across Banks Peninsula is shown in Figure C.2.

I chose fifty individuals as a minimum sample size to ensure replication across a number of life stages

without limiting the study to the largest populations. The initial aim of the surveys was to measure

variation in demographic parameters (including growth, survival and reproductive output) along a

climate gradient, over the course of one year. Two problems led to focussing solely on reproductive

output. Firstly, rock fall caused by the 2011 earthquake increased mortality, and plants were often

missing or in different locations upon return the following year. Furthermore, size and life stage of

surviving plants changed little between surveys. The growth rates and life expectancy of the species

was unknown prior to surveying, and more rapid change was expected.

Surveys took place during peak flowering; December 2010 for A. arboreum, February 2011 for

A. haworthii and March 2011 for C. orbiculata (all hereafter referred to as 2011), and at the same time

one year following (hereafter referred to as 2012). Where populations occurred on vertical surfaces,

e.g. cliffs or roadside cuttings, one 50 m permanent transect was placed at 1.4 m above the ground

adjacent to the vertical surface. At sites where the ground could be traversed (e.g. in grassland, only

applicable to C. orbiculata), five 10 m transects were placed at ground level at random points within

each population. At each site 50 plants were tagged with cable ties, selecting the closest plant to each

1 m interval, and a random subset of 10 flowering individuals were given numbered tags (or mature

plants if there were insufficient flowering plants). One Thermochron iButton® data logger was placed

at the mid-point along the 50 m transect, or the mid-point along the third 10 m transect, recording

temperature in degrees Celsius (°C). Data loggers were placed 5 cm above ground level, facing south,

with a protective covering of aluminium foil to protect from precipiataion and solar radiation.

Temperature was recorded at four-hourly intervals beginning at 00:00, and was accurate to the nearest

0.5 °C. I recorded GPS co-ordinates (WGS 1984) at both ends of each transect.

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Figure 4.1 Populations of a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata in

Banks Peninsula and New Zealand (inset), and locations of survey sites (green points, general region

labelled). Background layer shows annual precipitation, interpolated from Worldclim data, with

shaded relief [(Hijmans et al. 2005), available at http://www.worldclim.org/bioclim].

http://www.worldclim.org/bioclim

72

For each of the 50 plants tagged, I recorded life stage as one of four categories (Table C.2) and if

flowering, number of inflorescences. Life stage was intended for use in demographic measurements. I

estimated the number of rosettes for Aeonium species, based on the reported relationship between

branching modules and flowering (Jorgensen & Olesen 2000), and counted leaves along the main stem

for C. orbiculata. After preliminary data analysis, it was apparent that number of rosettes and leaves

were not reliable indicators of fecundity. In the second year of surveys, I additionally measured the

height, width and breadth (cm) of each tagged plant, approximated to canopy volume (L, equation 1).

Volume = [(height × width × breadth) ×10-3

] (1)

In both years, detailed measurements were taken from each of the ten flowering plants with numbered

tags. Umbels were counted on one randomly selected inflorescence per plant, flowers counted on three

randomly selected umbels, and flowers per inflorescence estimated (equation 2, x̅ = sample mean).

Flowers|inflorescence = x̅ (flowers|umbel) × (umbels|inflorescence) (2)

Because of the reported correlation of stem growth and flowering in Aeonium species, I measured the

previous years’ internode length and new growth since the end of the previous summer (mm). For

C. orbiculata, which lacks annual internodes, only canopy volume (L) was estimated.

4.3.4 Seed counts

In May 2011, before dehiscence, five inflorescences with fully developed seed pods were collected at

each site. Inflorescences were randomly selected from distinct plants and were individually sealed in

plastic bags for transport to the laboratory. In the laboratory, pods per inflorescence was estimated

using the same methodology as described for flowers per inflorescence (Section 4.3.3). Number of

seeds per pod was measured by weight based on sampling guidelines (International Seed Testing

Association 2008), on scales accurate to 100 µg. A homogenized 0.1 g sample of pod contents was

collected for each site. Aeonium inflorescences were sampled by emptying equal numbers of pods

from each until the mixed sample for each site reached 0.1 g. On average, 0.1 g equated to 50 pods of

A. arboreum and 55 of A. haworthii. Cotyledon orbiculata pods are larger (0.1 g equated to, on

average, 3 pods), so I instead emptied one pod from each inflorescence into the mixed sample.

Homogenized samples were separated into seed and chaff by eye, and the components weighed. The

average ratio of seed to chaff for each site was calculated using equation 3, where x = Seed to chaff

ratio, y = Pure seed weight of sample (g) and z = Total weight of sample (g).

x = y/z (3)

Next, 100 seeds were extracted from each mixed sample then weighed to estimate individual seed

weight. Number of seeds per pod was measured for three pods on each inflorescence. Pods were

randomly selected on the condition that they were closed and intact. Pods were emptied and content

73

weight was multiplied by the corresponding site seed to chaff ratio. The resulting pure seed weight of

the sample was divided by the individual seed weight to estimate seeds per pod.

4.3.5 Climate variables

Flowering and seed production were modelled against climate. The following variables were used:

frost days (below 0 °C), growing degree-days (GDD) at bases 5 and 10 °C, precipitation (mm),

modelled solar radiation (KWh/m2), elevation (MASL) and aspect (N, E, S, W or NA on flat terrain).

Growing degree days were chosen as plants generally respond to heat-sum variables (Wardlaw 1999),

and bases 5 and 10 chosen as they are commonly used for warm-loving species, and the species’

physiological limits were unknown. Number of frost days were used as the three species are thought to

be frost-sensitive (Vogan 2003). Precipitation was included because the species are succulent

xerophytes and may therefore be intolerant to excess precipitation (Jorgensen 2002), and solar

radiation on the basis that sunlight is fundamental to plant growth (Monteith 1972) and at least one

species is thought to be shade intolerant (Barker et al. 1997). Elevation appears to be a good predictor

of the species’ performance on Banks Peninsula (Chapter 3), although strong effects were not

expected because of the loss of high-elevation sites described previously. Aspect was used as a proxy

for solar radiation in the event that modelled solar radiation imperfectly captured site conditions, and

because the species are mostly absent from south-facing slopes on the Peninsula. Climatic variation

among survey sites is presented in Figure C.5. Temperature variables were calculated using data-

logger measurements collected at each site, while precipitation data were obtained from the CliFlo

database (National Institute of Water and Atmospheric Research 2014), using the nearest weather

station to each site (Figure C.4). Solar radiation was modelled over the same years as the surveys in

ArcMap 10.1, using the Solar Radiation Spatial Analyst tool (Fu & Rich 1999; Environmental

Systems Research Institute 2011) and a 15 m DEM base layer. In addition to climate variables, I also

included measurements related to maternal plant size, as the link to reproductive output is well-

established (Harper & White 1974). Specific size measurements were canopy volume (L), and for

Aeonium species, also internode length (mm).

Although peak flowering occurs at different times for each species, each climate variable was summed

over the same period for all three species. This was to facilitate model comparison among species and

incorporation into population models in subsequent chapters. All three species share a similar biology

(succulent, xerophyte, CAM) and phylogeny, so it was assumed they would respond to similar

climatic variables. Variables were summed over 6-monthly periods between the coldest month (July)

and December, which marks peak flowering in survey populations of A. arboreum and the beginning

of flowering for A. haworthii and C. orbiculata. To ensure that choice of time period did not affect

model results, models were also fitted with 6-monthly heat sums prior to survey date for each species,

and no differences in significant variables or model performance were found. It was not possible to

sum variables over the same period for models of seed production because it would require using

months before flowering or well after dehiscence for at least one of the species. Instead, seed

74

production was assumed to depend on conditions during flowering, due to pollinator availability and

climatic requirements for embryo development. Climate variables for seed models were summed over

the two-monthly peak flowering period relevant to each species (December - January for A. arboreum,

January - February for A. haworthii and February - March for C. orbiculata). Additionally, number of

pods per inflorescence was included as a variable under the hypothesis that vigorous plants would

invest more energy into flowers and seeds, and that more flowers would attract more pollinators.

4.3.6 Model fitting

The summing of variables over 6 months necessitated that flowering was modelled using 2012 data

only, as data loggers were not present at the sites prior to 2011 surveys. Having only one, or even two

years’ data is insufficient to test whether observations are representative of general trends. To address

this problem, variation was compared among years and sites, where large yearly differences would

demand less confidence in the generality of results. A one-way nested ANOVA tested for differences

among years and sites in number of inflorescences, flowers and seeds. Flowering data were nested by

Year│Site, and seed data by Site│Inflorescence. Differences in volumes and internode lengths among

individuals and sites were also tested using this method. Differences in total number of flowering

plants between sites were tested with a Chi-squared ANOVA [anova in base R (R Core Team 2014)]

run against binomial generalized linear models (GLMs) of all surveyed individuals. Binomial GLMs

were specified with the binary response variable Flowering, against the factor effects Site, and

Year + Site. Variables (y) were log-standardized according to equation 4 (�̅� = mean, s = standard

deviation).

Log Standardized y = {ln [yi] - �̅� [ln (y)]}/{2s [ln (y)]} (4)

Flowering and seed production were modelled using generalized linear mixed models (GLMMs) in the

R package lme4 (Bates et al. 2014; R Core Team 2014). For each species, the response variables

probability of flowering (P[Flower]), inflorescences per plant (Inflorescences│Plant), flowers per

inflorescence (Flowers│Inflorescence) and seeds per pod (Seeds│Pod) were modelled. I fitted

P[Flower] as a binomial GLMM, using data from all 50 tagged plants for the binary response variable

Flowering (excluding plants that died). I modelled Inflorescences│Plant, Flowers│Inflorescence and

Seeds│Pod as Poisson GLMMs. Two sets of models of Inflorescences│Plant were run for Aeonium

species: one using data from all flowering plants, the second using the 10 subset plants, as only the

subset data contained the predictor internode length. I tested whether Inflorescences│Plant within the

subset was representative of the overall within-site variation using a Kolmogorov-Smirnov test. For

C. orbiculata models of Inflorescences│Plant, all flowering plants were used. Flowers were only

counted in the subset surveys, so those data were used in Flowers│Inflorescence models. All

laboratory data were used for Seeds│Pod models.

75

Mixed models (GLMMs) contain random effects to account for pseudo-replication in the sampling

design and associated unexplained variation, where separate intercepts are fitted for each random

effect specified. For flowering models I specified Site as a random effect, and for seed models

Inflorescence nested within Site. All except binomial models also had a random effect, Odis, to correct

for overdispersion (Harrison 2014), where Odis is a vector of 1: n (n = number of samples). All

climatic variables were standardised to a mean of zero and standard deviation of one, while plant size

variables were log-standardized in the same way as for ANOVA variables. Model parameters (climatic

and non-climatic variables) were tested against null models individually using a Chi-squared test.

Significant variables were then added to the final model and removed in a backwards stepwise fashion.

Model fit was assessed by calculating the marginal and conditional R2 of each final model using the

methods of Johnson (2014). This function estimates pseudo-R2 using random and fixed effects

(conditional), and fixed effects only (marginal). Marginal and conditional R2 allow comparison

between the amount of variation explained by variables of interest (fixed effects), unexplained

differences between sampling units (random effects) and noise. For models of P[Flower], I calculated

the area under the receiver operating curve (AUC) with 95% confidence intervals, in the R package

pROC (Robin et al. 2011; R Core Team 2014). The AUC conveys whether models are better at

identifying true positives and negatives than chance without requiring a probability threshold, and is

arguably a better measure of fit for binary data than R2. All fixed effect coefficients are reported with

95% confidence intervals, calculated using the confint.merMod function in lme4, with 500

bootstrapped replicates. Random effects are presented as mean, minimum and maximum values.

4.3.7 Model predictions

Mean seeds per capita were estimated as the product of mean predicted inflorescences, flowers and

seeds of each species. All mean values in the text are reported ± standard error (SE). For predictions,

continuous parameters (e.g. mean volume of flowering plants) were set to mean values across all

flowering plants, and the most representative category chosen for categorical variables (e.g. aspect).

Confidence intervals were generated by bootstrapping each model 1000 times. Within each bootstrap

replicate, predicted inflorescences, flowers and seeds were multiplied and the 1000 resulting values

used to estimate mean seeds per capita and 95% confidence intervals. This stepwise method allowed

prediction error to be compounded at each level of multiplication where models were non-

independent. To measure the relative influence of each model parameter on total predicted seeds, I

calculated elasticity values for each parameter. This identified potential driving variables of total

fecundity on Banks Peninsula and which level of fecundity (e.g. seed or flower production) may be

most limiting for the species. This definition of elasticity is used widely in economics, and was

calculated according to equation 5, where Y= Predicted seeds per capita, X = Input parameter value

and Δ is the change relative to the baseline. Parameters were altered relative to the baseline values

used to predict mean seeds per capita. Continuous variables were changed between - 100% and

76

+ 100% of the baseline, and categorical variables were calculated for each separate value. The gradient

of the smoothed line of the % change in Y vs X is the reported elasticity.

Elasticity = (% Δ Y)/(% Δ X) (5)

4.4 Results

4.4.1 General patterns

At all but one site, 50 plants were tagged in the first year (total plants tagged in 2011 = 374 for

A. arboreum, 400 for both A. haworthii and C. orbiculata). One A. arboreum site had fewer than 50

plants tagged due to small population size and lack of alternative survey sites. At all sites, 10 plants

(80 in total) were sub-sampled for detailed measurements in 2011. However, of those 80 plants, only

24 A. arboreum, 30 A. haworthii and 44 C. orbiculata were re-sampled in 2012, and so the sample size

for models of flowers and inflorescences was reduced. This was due partly to high mortality rates,

primarily affecting Aeonium plants (Table 3.1). Mortality was higher for both Aeonium species than

for C. orbiculata, but only a minority of deaths could be confirmed (where a plant could not be re-

located in 2012, it was assumed dead). Mortality was highest for A. arboreum, as 50% of sites

experienced moderate or large rock falls, where some or most of the cliff face had fallen away (Table

C.1). Sample sizes were further reduced by the fact that not all flowering individuals tagged in 2011

flowered in 2012. Some flowered in only one of the two years, but a high proportion of Aeonium

plants, and the majority of C. orbiculata, flowered in both (Table 4.1). In 2011, 17% of all

A. arboreum plants surveyed produced flowers, and 9% in 2012. For A. haworthii in 2011 vs. 2012,

18% vs. 12% of plants flowered, and 35% vs. 42% for C. orbiculata. Binomial GLMs indicated

significant differences between years in number of flowering plants for A. haworthii and C. orbiculata

(Table 4.2). There was no significant yearly variation in Flowers|Inflorescence in any of the three

species, or Inflorescences|Plant in A. arboreum. There were significant and strong site differences in

all variables except Flowers|Inflorescence of A. arboreum. Boxplots of raw data (Figure C.6) indicate

that the lack of significant site differences in this case may be due an extremely wide distribution of

flowers per inflorescence at one site (CHB2). There were significant differences in Seeds|Pod among

inflorescences and sites in all three species, with highest variation among sites.

4.4.2 Flowering probability

There were large among-site differences in proportion of flowering individuals: 0 - 23% of tagged

A. arboreum flowered in 2012, and A. haworthii was similar, ranging from 2 - 36%. There were higher

proportions of flowering plants in C. orbiculata than either Aeonium species, varying between 8 - 65%

among sites (Figure C.6). The best predictor of P[Flower] in all three species was canopy volume.

Climatic variables were not good predictors of flowering when used alone for any of the species

(marginal R2 < 0.2), and were not significantly better than null models for either Aeonium species.

Models including canopy volume for A. arboreum and C. orbiculata were significantly improved by

77

Table 4.1 Total numbers of Aeonium arboreum, A. haworthii and Cotyledon orbiculata flowering in 2011 (Y1) or 2012 (Y2) only, or both years. Mortality shown as

% of all individuals, broken down into number of plants confirmed dead vs. not re-located. Number of samples for each models also provided.

Species Total no. flowering Mortality n (samples) in model

Y1 only Y2 only Both Confirmed Not found Total P[Flower] (Inflorescences│plant) (Flowers│inflorescence) (Seeds│pod)

A. arboreum 38 10 25 84 20 28% 269 24 24 122

A. haworthii 39 14 35 17 49 16% 335 29 30 123

C. orbiculata 31 59 110 6 18 6% 373 180 61 120

Table 4.2 Analysis of variance (ANOVA) source tables, showing differences in fecundity among years (if applicable), sites, and plants (if applicable) for Aeonium

arboreum, A. haworthii and Cotyledon orbiculata. ANOVAs run for numbers of log-standardised Inflorescences|Plant, Flowers|Inflorescence, and Seeds|Pod. For

total numbers flowering, columns show degrees of freedom, deviance, and residual degrees of freedom and deviance from a Chi-squared ANOVA of a binomial

GLM with year and site effects. Significant results highlighted in bold and level denoted by asterisks (*), where; * p < 0.05, ** p < 0.01, *** p < 0.001.

Species Source Total number flowering Inflorescences|Plant Flowers|Inflorescence Seeds|Pod

DF Dev RDF RDev DF SS00 MS F ***** DF SS MS F *** DF SS MS F ***

A. arboreum Year 1 01.9 641 540.1 *** 1 5 x 10-3

5 x 10-3

0.1 ***** 1 00.8 0.8 3.4 ***

Site 7 39.2 634 500.9 *** 6 12.300 2.100 21.4 ***** 6 02.8 0.5 2.1 *** 7 21.8 3.100 84.2 ***

Plant 32 05.4 0.200 04.6 ***

Resid 69 6.600 0.100 69 15.4 0.2 82 03.0 3 x 10-2

A. haworthii Year 1 04.3 734 720.5 *** 1 1.400 1.400 7.4 ***** 1 00.5 0.5 2.2 ***

Site 7 52.9 727 667.5 *** 7 5.400 0.800 4.0 ***** 7 03.8 0.5 2.4 *** 7 13.0 1.900 170.5 ***

Plant 33 16.6 0.500 046.2 ***

Resid 82 15.700 0.200 82 18.2 0.2 82 00.9 0.100

C. orbiculata Year 1 11.8 770 1039.7 *** 1 1.500 1.500 6.6 ***** 1 00.2 0.2 1.1 ***

Site 7 81.5 763 958.3 *** 7 3.700 0.500 2.4 ***** 7 07.7 1.1 5.4 *** 7 11.0 1.600 011.2 ***

Plant 32 07.5 0.200 001.7 ***

Resid 125 28.100 0.200 125 25.4 0.2 80 11.2 0.100

78

(a) (b)

(c) (d)

(e) (f)

Figure 4.2 Coefficients and predictions of P[Flower] GLMMs for Aeonium arboreum (a, b),

A. haworthii (c, d) and Cotyledon orbiculata (e, f). Fixed effect coefficients shown with 95%

confidence intervals (solid points), random effects with maximum and minimum values (hollow

points). Plots b, d and f show modelled probability of flowering vs. canopy volume (lines). Axis

rescaled to ∛(Volume×103), ≈ plant height, for aesthetics. Proportion of plants flowering at midpoints

of volume bins shown (points) with number of plants in bin (numbers).

79

the inclusion of, respectively, GDD10 and solar radiation, although canopy volume remained the

principal explanatory variable (Figure 4.2a-c). Model predictions using mean climate variables where

necessary, show that Aeonium plants were more likely to flower than not (P[Flower] >0.5) when

plants exceeded approximately 200 L. The same threshold for C. orbiculata was approximately 6 L.

Models of P[Flower] had high explanatory power; marginal R2 were 0.75, 0.73 and 0.67 for

A. arboreum, A. haworthii and C. orbiculata respectively. Models consistently assigned higher

P[Flower] to flowering over non-flowering plants (AUC = 0.91 ± 0.04 for A. arboreum, 0.94 ± 0.03

for A. haworthii and 0.91 ± 0.03 for C. orbiculata).

4.4.3 Inflorescences per plant

In 2011, across all sites A. arboreum produced a mean of 4.7 ± 0.8 (± SE) inflorescences per plant,

between a minimum of 1 and maximum of 13. Aeonium haworthii individuals produced fewer

inflorescences on average; 3.8 ± 1.0, but had a wider range between 1 and 29. Cotyledon orbiculata

produced more inflorescences than Aeonium species, with a mean of 9.1 ± 2.1 and between 1 and 88

per plant. For GLMMs of A. haworthii and C. orbiculata, it was necessary to remove the maximum

observed value (one outlier for each model), as they strongly biased the results. Models of

Inflorescences|Plant were run for Aeonium species using both the full and sub-sampled datasets, as the

sub-sampled dataset also included internode length as a potential variable. The sub-sampled data

appeared to be representative of wider within-site variation; Kolmogorov-Smirnov tests on

Inflorescences|Plant revealed no significant differences between the two distributions. Variables

related to plant size were the best predictors of number of inflorescences (Figure 4.3), specifically

previous internode length for A. arboreum, and canopy volume for C. orbiculata. None of the

variation in A. haworthii could be explained. Climate variables alone did not perform better than a null

model for Aeonium species, and although precipitation performed better than null for C. orbiculata, it

explained little variation (marginal R2 < 0.1). The model for C. orbiculata predicted that larger plants

produce more inflorescences (Figure 4.3d), while for A. arboreum higher stem growth in the previous

year (longer internodes) predicted more inflorescences the following year (Figure 4.3c). It should be

noted that internodes reflect growth from approximately May to April, with the main growing season

in winter (Jorgensen & Olesen 2000). Therefore, the “new growth” measured at the time of surveying

reflects less than a full years’ growth, which may explain why it is a poor predictor compared with

previous years’ internodes. Model fit for Inflorescences|Plant was lower than for P[Flower], with

marginal R2 of 0.42 and 0.53 for A. arboreum and C. orbiculata, respectively. Conditional R

2 values

were also low (0.56 and 0.59) indicating high noise in both datasets.

4.4.4 Flowers per inflorescence

Aeonium arboreum produced, on average, 534 ± 49 flowers per inflorescence in 2012 (mean ± SE),

between minimum of 108 and maximum of 2544. In contrast to the Inflorescences|Plant results,

A. haworthii produced fewer flowers then A. arboreum; on average 161 ± 17, between 15 and 357

80

observed per inflorescence. Cotyledon orbiculata inflorescences produced the fewest flowers on

average (137 ± 24) but ranged from 5 to a maximum of 630. There was no correlation between

Flowers|Inflorescence and canopy volume or internode length in either Aeonium species. For

A. arboreum, only aspect predicted number of flowers better than a null model, with slightly more

flowers at west-facing sites, while north and east-facing sites were similar (Figure 4.4a & c). There are

no predictions for south-facing aspects as none of the sub-sampled plants flowered in either year at the

south-facing site. Again, none of the variation in A. haworthii could be explained. For C. orbiculata,

Flowers|Inflorescence was best explained by canopy volume alone, and climate variables did not

perform better than a null model, either in isolation or in addition to canopy volume. Performance of

Flowers|Inflorescence models was the lowest in the study, with marginal R2 of 0.29 for A. arboreum

and 0.35 for C. orbiculata. Similar to Inflorescences|Plant, conditional R2 values were also low (0.29

and 0.37), indicating a high degree of noise in the data not attributable to random or fixed effects.

(a) (b)

(c) (d)

Figure 4.3 Outputs of Inflorescences|Plant GLMMs for Aeonium arboreum (a, c) and Cotyledon

orbiculata (b, d). Plots a & b show model coefficients, solid points for fixed effects ± 95% confidence

intervals, hollow for random effects with maximum and minimum values. Plots c & d show predicted

inflorescences (lines) vs. previous internode length (mm) and canopy volume (L), for A. arboreum (c)

and C. orbiculata (d). Canopy volume axis rescaled to ∛Volume × 103 (≈ plant height) for aesthetics.

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(a) (b)

(c) (d)

Figure 4.4 Outputs of Flowers|Inflorescence GLMMs for Aeonium arboreum (a, c) and Cotyledon

orbiculata (b, d). Plots a & b show model coefficients, solid points for fixed effects with 95%

confidence intervals, and hollow for random effects with maximum and minimum values. Plot c shows

predicted number of A. arboreum flowers (triangular points) versus aspect, with observed values in

boxplot. Plot d shows predicted number of C. orbiculata flowers (line) versus canopy volume (L).

Axis rescaled to ∛Volume × 103, ≈ plant height, for aesthetics, observed values shown as points.

4.4.5 Seed production

Seed samples indicated that in 2011, Aeonium species produced smaller seeds and more chaff than

C. orbiculata. Seeds of A. arboreum were lightest at an estimated 20 µg per seed, with A. haworthii at

26 µg, and C. orbiculata at 29 µg. Mean percentage (± SE) of pure seed was similar for both Aeonium

species (32 ± 6 % for A. arboreum and 31 ± 6 % for A. haworthii), and much higher for C. orbiculata

at 66 ± 6 %. There was considerable variation among sites, with a range of 9 – 51% pure seed for

A. arboreum and 3 – 55 % for A. haworthii. In contrast, C. orbiculata varied between 39 - 100% pure

seed among sites. Climatic variables did not explain among-site variation, although with only one

sample per site, low degrees of freedom are limiting. Mean number of Seeds|Pod was higher in

C. orbiculata than either Aeonium species. On average, A. arboreum produced 31 ± 2 seeds per pod,

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(a) (b)

(c) (d)

(e)

Figure 4.5 Outputs of Seeds|Pod GLMMs for Aeonium arboreum (a, c) and Cotyledon orbiculata (b,

d) and legend for plots c & d (e). Plots a & b show GLMM coefficients, solid points for fixed effects

with 95% confidence intervals, hollow points for random effects with maximum and minimum values.

The reference category for aspect is north. Plots c & d show predicted number of seeds per pod, versus

pods per inflorescence, in A. arboreum and C. orbiculata respectively. Lines show predictions for

aspect category, points show observed data (see legend).

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and A. haworthii produced 23 ± 2. In contrast, C. orbiculata produced on average 812 ± 56 seeds,

thanks to higher ratios of seed to chaff and larger pods. Again, no variables explained variation in

A. haworthii, whereas the best models for A. arboreum and C. orbiculata were identical; the best

explanatory variable was aspect (Figure 4.5a & c), with a marginal R2 of 0.59 (A. arboreum) and 0.31

(C. orbiculata) when used alone. Models were improved significantly by the inclusion of pods per

inflorescence, although it explained less variation than aspect (marginal R2 of 0.14 for A. arboreum

and 0.04 for C. orbiculata when used alone). Plots indicated a clear interaction effect between the two

variables (Figure 4.5d & e), which was incorporated into the final models.

In general, pods per inflorescence and seeds per pod were positively correlated for both A. arboreum

and C. orbiculata. In the case of A. arboreum the effect was strongest at west-facing, and to a lesser

extent, east-facing sites. North and south-facing sites showed little to no relationship with pods per

inflorescence, where seed numbers are predicted to be low, and near constant. For C. orbiculata,

similar patterns occurred, but north and east-facing sites were more favourable and strongly related to

pods per inflorescence, with west and “none” (i.e. flat gradient) close to constant (Figure 4.5c & d).

Seed models performed better for A. arboreum than C. orbiculata, but for both species fixed effects

explained most of the non-random variation; marginal vs. conditional R2 values were 0.66 vs. 0.83 and

0.40 vs. 0.44 for each species respectively. There was a disparity between number of flowers per

inflorescence in section 4.4.4 and number of pods per inflorescence in seed samples. This could have

arisen from loss of pods after flowering or during transport, or because of sampling bias.

Consequently, caution is warranted if extrapolating these models to higher numbers of seeds per pod.

4.4.6 Site differences in canopy volume

Table 4.3 Source tables for one-way ANOVAs on among-site differences in log-standardized canopy

volume and internode length, for Aeonium arboreum, A. haworthii and Cotyledon orbiculata.

Analyses were run on second year data, both across all plants, and flowering plants only.

Species Source Canopy volume

(all plants)

Internode length

(flowering plants)

Canopy volume

(flowering plants)

DF SS MS F *** DF SS MS F * DF SS MS0 F ***

A. arboreum Site 7 03.5 0.5 02.0 *** 6 2.8 0.5 2.8 * 6 00.9 0.200 6.5 ***

Resid 238 57.8 0.2 17 2.9 0.2 25 00.6 2 x 10-2

A. haworthii Site 7 21.2 3.0 15.9 *** 7 3.6 0.5 3.1 * 7 00.6 0.100 2.4 *** Resid 327 62.3 0.2 22 3.6 0.2 46 01.7 4 x 10

-2

C. orbiculata Site 7 09.2 1.3 05.7 *** 7 07.2 1.000 4.7 ***

Resid 365 83.4 0.2 172 37.6 0.200

Because plant size was a strong predictor at most reproductive stages, among-site differences in

canopy volume (and internode length for Aeonium species) were investigated. In all three species,

whether including all plants or just those flowering, there were significant differences among sites. I

attempted to explain this site variation by running Gaussian GLMMs with a random site effect against

climate variables, but found no significant relationships.

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4.4.7 Total per capita fecundity

Predicted numbers of inflorescences, flowers and seeds were combined to predict mean seeds per plant

(Table 4.4). Where aspect was a parameter I selected the aspect category which, if extrapolated, would

represent favourable sites but without trending to extreme values (Figure 4.5c & d): for A. arboreum I

selected east, and C. orbiculata, none. All predictions for A. haworthii were derived from null models

representing means across all sites. Models predict that of the three species, C. orbiculata produces the

most seeds per plant on average, due to numerous seeds per pod. Aeonium haworthii, meanwhile, is

predicted to produce the fewest seeds; as although the species produces more inflorescences than

A. arboreum, its inflorescences produce fewer flowers.

Table 4.4 Predicted mean inflorescences per plant, flowers per inflorescence and seeds per pods for

Aeonium arboreum, A. haworthii and Cotyledon orbiculata, with 95% bootstrapped confidence

intervals in brackets. Models use mean plant volume or internode length of all flowering plants, aspect

set to east (A. arboreum) or none (C. orbiculata). Seeds per plant is the product of the three models.

Species Inflorescences Flowers Seeds Seeds per plant

A. arboreum 5 (3 - 6) 254 (179 - 349) 022 0(12 - 36) 025 826 0(10 480 - 52 501)

A. haworthii 3 (2 - 4) 132 (102 - 167) 0130 (7 - 24) 004 510 0 (2 118 - 8 922)

C. orbiculata 5 (4 - 6) 0710 (52 - 97) 521 (360 - 782) 191 862 (104 562 - 364 852)

Elasticities of GLMM parameters were calculated in reference to their effect on predicted seeds per

plant. I tested all parameters in final models of inflorescences, flowers and seeds, for A. arboreum and

C. orbiculata. For both species, aspect had most effect on predicted seeds per capita (Table 4.5). For

A. arboreum, the effect of aspect on seeds per capita was strongest at the level of flowers per

inflorescence. For C. orbiculata, only models of seeds per pod contained an aspect term, so variation

at this level had the greatest effect on seeds per capita. Plant size parameters (i.e. internode length,

volume and pods per inflorescence) had a minor effect on predicted seeds per capita at all levels of

fecundity (inflorescences, flowers and seeds).

Table 4.5 Parameter elasticity values for GLMMs of inflorescences per plant, flowers per

inflorescence and seeds per pod, calculated against predicted seeds per plant for Aeonium arboreum

and Cotyledon orbiculata. Highest elasticity value per species is highlighted in bold.

Model Parameter A. arboreum C. orbiculata

Inflorescences|Plant Internode 1 0.14

Volume 00.53

Flowers|Inflorescence Aspect 8.31

Volume 00.23

Seeds|Pod Pods|Inflorescence 0.79 00.34

Aspect 4.11 21.62

Aspect*Pods|Inflorescence 1.65 -3.70

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4.5 Discussion

4.5.1 Direct climate limitation

Reproductive traits of A. arboreum, A. haworthii and C. orbiculata were highly variable among and

within sites, and direct relationships with climate were weak across naturalized populations on Banks

Peninsula. These are similar to the findings of Jorgensen (2002), who reports that vegetative and

reproductive traits of four Canarian Aeonium species have a high degree of variability not explained

by plant size, climate or phylogeny. Despite high noise in the data, probability of flowering in

A. arboreum correlated positively with heat sum (GDD10), and plants at west-facing sites tended to

produce more flowers per inflorescence and seeds per pod than at other aspects. Cotyledon orbiculata

was more likely to flower at sites with higher modelled solar radiation, and pods contained most seeds

at north-facing sites. These findings are consistent with the biogeography of the three species; all three

originate in warmer climates than New Zealand, and Banks Peninsula represents the cooler extremes

of their distributions (Chapter 2). Furthermore, Cotyledon orbiculata is likely to be shade intolerant as

a result of its photoprotective epicuticular wax (Barker et al. 1997), which both Aeonium species lack

(Stevens 1995). Although a slight effect of climate was observed on probability of flowering, no

evidence was found that climate was limiting to reproduction as would be expected in marginal

populations (i.e. seed was produced in large quantities at all sites).

In the case of A. haworthii, I was unable to explain variation in any reproductive trait except

probability of flowering, despite large and highly significant differences among sites. In particular,

among-site variation in number of seeds per pod was twice as high for A. haworthii as for A. arboreum

(F-values of 170.5 vs. 84.2), yet there were no correlations between A. haworthii seeds per pod and

climatic or non-climatic variables. This could be due to limitations in the survey design, which are

discussed in detail later. However, the sampling design was identical for all three species, and

variation was at least partially explained for all reproductive traits of A. arboreum and C. orbiculata.

As an alternative explanation, reproductive traits of A. arboreum might exhibit stronger responses to

plant size and climate than A. haworthii because of their evolutionary niches. Lems (1960)

hypothesizes that A. arboreum is part of an older lineage of Aeonium than A. haworthii based on their

respective growth forms, and that “older” forms which take longer to reach flowering maturity and

produce larger inflorescences are adapted to milder, more stable climates in the native range. He

argues that the group containing A. haworthii, which are found at higher elevations and more extreme

conditions in the Canary Islands, flower at a younger age (producing fewer seeds per capita, as

observed in this study) to maximise chances of reproduction in harsh climates. If this is the case,

A. haworthii reproduction should be more adaptable to climate than A. arboreum.

According to sensitivity analyses, heat sum (GDD10) and solar radiation had minor impacts on per

capita seed output compared with aspect. It was surprising that aspect was selected repeatedly as a

significant variable over other, more biologically meaningful variables. Aspect was included in the

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potential variables only as a proxy for solar radiation, in the event that the ArcMap model imperfectly

captured real site conditions. Error in the model is one possible explanation for the importance of

aspect. Alternatively, aspect could capture other variables related to solar radiation but imperfectly

captured by total insolation (e.g. mid-day sun versus morning or afternoon sun). Because all three

species flower in spring/summer they are assumed to be long-day plants (LDPs), and floral initiation

by far-red light (which is higher in morning and afternoon) has been documented in a number of other

LDPs (Taiz & Zeiger 1991). Many other environmental variables vary with aspect, but few are likely

to affect the study species at the particular sites surveyed. One of these few is salinity: most sites were

in the northern bays of the Peninsula, so perhaps north-facing sites tended to have higher salinity and

sea spray. Alternatively, Lems (1960) reports that A. arboreum thrives on northeast facing slopes in

the Canary Islands where plants are exposed to the humid trade wind. However, in this study

A. arboreum performed better at west-facing sites, and in Canterbury the humid, prevailing wind is

easterly (McGann 1983) while the characteristic “nor’wester” foehn wind is hot and dry (McGowan &

Sturman 1996). As a consequence of how solar radiation and wind patterns change with aspect, soil

moisture and organic matter also vary. In North Canterbury, soil on north-facing slopes is usually drier

than on south-facing slopes (Radcliffe & Lefever 1981). Although soil may seem irrelevant to cliff-

dwelling species, they often grow in small pockets of organic matter on rock faces. Equally, biotic

interactions may vary with aspect: pollinators are often more active on sunny slopes (Weiss et al.

1988), and differences in community structure and vegetation may increase competition (Bennie et al.

2006; Warren II 2010). Jorgensen (2002) describes growth limitation in other Aeonium species with

increasing longitude in the Canary Islands, hypothesized to reflect decreasing solar radiation and

higher light competition. Overall, while aspect appears to be important and potentially limiting for

A. arboreum and C. orbiculata at the study sites, the underlying mechanism is unclear and

extrapolation of these results to other regions is discouraged.

4.5.2 Plant size – indirect climate limitation?

While direct relationships with climate were weak, plant size was a predictor of at least one

reproductive trait in all three species. In most cases, canopy volume (L) was a better predictor than

internode length (mm) or number of leaves/rosettes, neither of which correlated with volume. Only in

one model of inflorescences per plant (A. arboreum) was internode length a better predictor than

volume. Internode position (reported to correlate negatively with internode length) has been used to

predict flowering probability in A. haworthii (Jorgensen & Olesen 2000), so it was surprising that

length was a poor predictor. Despite its apparent importance, the relationship between plant size and

reproductive traits is ambiguous. On one hand, positive size-fecundity relationships are found in many

plant species (Aarssen & Taylor 1992), and some argue that it is a near-universal phenomenon

(Herrera 1991). In turn, larger plants may attract more pollinators (Wyatt 1980; Gerber 1985),

although flowers sometimes receive proportionally fewer visits (Klinkhamer et al. 1989; Herrera

1991). A site containing small individuals as a result of chance, non-climatic effects (e.g. competition)

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or being more recently colonized (i.e. with many young individuals) should therefore produce fewer

seeds per capita regardless of climate. Yet, the observed size-fecundity relationship could be an

indirect result of climate (perhaps higher temperatures favour faster growth, or plants struggle to reach

a minimum reproductive size in harsh environments).

Whether the size-fecundity relationship is a result of climate, demography or both, is unclear. I

investigated by testing for significant differences among sites in all plants, and flowering plants only.

There were significant differences among sites in canopy volumes of flowering A. arboreum

individuals, but not in volumes of all plants. In other words, plants flowered at smaller sizes at some

sites than at other sites. The size-fecundity differences among A. arboreum sites are therefore unlikely

to be simply a result of population structure or chance. If some sites simply had many small, young

plants size differences would be expected across populations as a whole, not just in flowering plants.

However, this analysis alone cannot distinguish which sites are more favourable, as plants may also

flower when small because of stress (Wada & Takeno 2010). In contrast, there were significant

differences in plant size among overall populations and among flowering plants in both A. haworthii

and C. orbiculata. This could indicate that in favourable climates growth is faster (thus, many

individuals are large), and that plants flower when smaller under good conditions. But, population size

structure may vary among the survey sites for numerous other reasons. These include variation in soil

characteristics (some sites were loess banks, while others were bare rock), distance from shoreline and

salinity, wind patterns, or disturbance (most notably, landslides). Rock type may be particularly

important to these geophytic species, and the surveys covered seven geological units roughly grouped

into loess, volcanic rock and gravel (Table C.1). Without prior knowledge on the effect of rock type on

the study species, it is difficult to speculate as to its importance, although application of silicates has

been shown to boost growth in Kalanchoe Adans. (MoonSook et al. 2012).

4.5.3 Implications for spread, and limitations

There are notable limitations to this study that reduce the generality of the results and that may have

weakened detection of climatic effects. Peak flowering for each species was assumed to occur at the

same time across sites, but climate is heavily linked with floral initiation [in addition to other variables

e.g. day length (Taiz & Zeiger 1991)]. Sampling may therefore have occurred before peak flowering at

some sites. Variation within both Aeonium species was particularly high, perhaps exacerbated by the

frequency of natural hybrids. This is especially true for A. arboreum, which overlaps phenologically

with A. undulatum [also common on the Peninsula (Webb et al. 1988)]. As a result, defining

populations as belonging to one taxonomic unit can be troublesome. It is also possible that sampling

plants near ground level has biased results for cliff populations; reproductive output at ground level

could be unrepresentative of higher microsites where competition might be lower. The lack of strong

climatic responses could indicate that other variables, e.g. relative humidity, are more limiting than

temperature, precipitation or radiation. Even if the variables used were limiting, perhaps the time

periods used for calculating sums were not the most appropriate, or microclimate variation within sites

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was high and not captured by the data-loggers. Similarly, precipitation data were obtained from the

nearest weather station, decreasing statistical power and accuracy in capturing rainfall at survey sites.

The lack of accessible large populations resulted in sampling a climate gradient that, apparently, was

insufficiently wide. Furthermore, the generality of the conclusions is lessened by having a single year

of data and temporal extrapolation of these results is discouraged.

Limitations aside, it is possible to draw some inferences from the data. There was no evidence of

limited fecundity in any sampled populations of A. arboreum, A. haworthii or C. orbiculata on Banks

Peninsula. Namely, plants readily flowered and produced viable seeds at all sites, and direct climatic

effects were minimal, contrary to expectations if some were marginal or edge populations. There were

significant among-site differences in plant size and reproductive traits where plant size, growing

degree-days and solar radiation had a minor impact on seeds per capita compared with aspect. The

most potentially limiting reproductive trait for spread appears to be seeds per pod, as observed values

had a wider range than number of inflorescences or flowers. Upper and lower 95% confidence

intervals of mean seeds per pod differed by a higher factor than flowers or inflorescences, in all three

species. Seed production is likely to influence spread of all three species strongly, as they are wind-

dispersed, produce very small seeds with limited energy reserves, and evidence suggests potentially

low rates of germination (Alamo et al. 1996).

There were also marked differences in mean predicted seeds per capita between the three species. The

average Aeonium arboreum plant is predicted to produce over five times as many seeds as

A. haworthii. This was surprising as both species have been naturalized for the same amount of time

and have developed similar distributions. However, predicted Aeonium seeds per capita were

consistent with the hypothesis of Lems (1960) that growth-form classes containing A. haworthii

should flower younger and produce fewer seeds than those containing A. arboreum, as adapted

responses to their native niches. In contrast, Cotyledon orbiculata produces many more seeds than

either Aeonium species, over a predicted 190 000 per plant on average, across sampled populations. It

is interesting to note that mean seeds per pod was lower than reported from open pollination

experiments in the native range [521 vs. 1050 seeds per pod (Zietsman 1998)]. Cotyledon orbiculata

has a much wider distribution in the region than either Aeonium species, and while additional factors

may also have facilitated its spread (e.g. broader climatic tolerances and habitat preferences), high

seed output is likely to have contributed significantly. From a management perspective, relatively

small populations of C. orbiculata still constitute a considerable seed source, and could facilitate

continued invasion subject to dispersal and germination.

4.5.4 Conclusions

The aims of this chapter were to assess evidence for direct or indirect climatic limitation to fecundity

in the three study species, across their current ranges on Banks Peninsula. I found evidence of weak

direct climatic responses in probability of flowering in all three species, but insufficient evidence to

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conclude that fecundity is strongly climate limited within their current ranges. A strong relationship

with plant size was found in all three species, but it is unclear whether this is an indirect response to

climate. I also aimed to answer which stage of fecundity, and which variables, were most limiting to

reproduction. In all three species, per capita seed output was most sensitive to variation in seeds per

pod due to a wider range of observed values. Meanwhile, the variable with the greatest effect on

A. arboreum and C. orbiculata seeds per capita was aspect, although it is unclear why some aspects

are more favourable than others to the species. I was unable to explain variation in flowers,

inflorescences or seeds produced by A. haworthii. The final aim was to assess whether more

widespread species had highest fecundity, and there is some support for this hypothesis. Cotyledon

orbiculata produces more seeds than either Aeonium species, a difference of 2 - 3 orders of magnitude.

Nevertheless, A. haworthii produces fewer seeds than A. arboreum despite their similar distributions.

Though the species’ invasion success cannot be explained by fecundity alone, high seed production by

C. orbiculata is likely to facilitate spread and merits consideration for control efforts.

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Chapter 5 – Validating SDM projections against field data

5.1 Abstract

Correlative species distribution models (SDMs) are valuable tools in invasion ecology, but assessing

the accuracy of their projections is not always straightforward. While the underlying algorithms are

becoming increasingly sophisticated, the methods used to validate SDM projections remain largely

static. Models of potential distributions are usually validated against occurrence data, but testing

hypothetical scenarios against current conditions unfairly rewards over-fitted models. Instead, species’

performance data and process-based models can be utilized to test and improve SDM projections. In

this chapter, the concept of fundamental absences (where a species cannot occur due to limiting abiotic

conditions) is introduced. Using this concept, I develop a novel approach to validating and refining

SDM projections against climate-driven population models. Population models were used to predict

whether climatic conditions in Banks Peninsula, New Zealand are conducive to self-sustaining

populations of three non-native succulent species; Aeonium arboreum, A. haworthii and Cotyledon

orbiculata. Pre-existing field data detailing how growth, mortality, germination and fecundity respond

to climate were incorporated into an integral projection model (IPM), which was used to predict

hypothetical population growth at 83 occupied and unoccupied locations in the region. Predicted

population growth was used to infer fundamental presences and absences and to validate previous

SDM projections of climatic suitability. Finally, SDM projections were refined to increase parsimony

with IPM predictions. The results of this independent validation showed that the SDMs performed

better than k-folds cross-validation using only occurrence data would suggest. Nonetheless, the SDMs

over-predicted suitable climate, and I identify likely sources of error leading to the over-prediction.

The use of validation techniques similar to those presented is encouraged in field of distribution

modelling.

Keywords: BIOCLIM, IPM, population modelling, SDM, validation

5.2 Introduction

Advances in computing power have given ecologists access to a suite of methods for predicting how

species respond to their environment. The most commonly used of these methods are correlative

species distribution models [SDMs (Elith 2013)]. User-friendly software and freely-available input

data make it relatively easy to project environmental suitability for a species (Ahmed et al. 2015), but

despite a recent explosion in the SDM literature, there is ongoing debate around how trustworthy the

ensuing projections are (Pearson & Dawson 2003; Jeschke & Strayer 2008; Sinclair et al. 2010;

Warren 2012). There are a number concerns regarding the accuracy of SDM projections. For example,

although it is well known that SDMs are sensitive to changes in input settings; such as sampling area

(Merow et al. 2013), pseudo-absence sampling (Senay et al. 2013), corrections for bias (Syfert et al.

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2013) and choice of environmental predictors (Araújo & Guisan 2006), these details are often omitted

from published articles, preventing critical evaluation of their results (Yackulic et al. 2013).

Furthermore, it is well-known that modellers should base their choice of algorithm on the ecology of

the target species and question at hand (Aguirre-Gutiérrez et al. 2013; Kriticos et al. 2013). Yet, a

survey of the modelling community found that SDMs are overwhelmingly chosen based on

convenience (Ahmed et al. 2015), with algorithms developed in R (R Core Team 2014) and MaxEnt

(Phillips et al. 2006) being most popular. Lozier et al. (2009), in a satirical exercise modelling

Sasquatch distributions, draw attention to how easily spurious SDM results can be confused with

meaningful ones when the species’ biology is disregarded.

Aside from human error, SDMs have been criticized because of questionable underlying assumptions.

These include the assumption that, 1) the environmental variables used correlate with and are

representative of the species’ requirements, 2) that these requirements are the same across space and

time (Elith & Leathwick 2009), 3) that the species distribution is at equilibrium with the environment

(Václavík & Meentemeyer 2012), and, 4) that adaptation and niche shifts are not occurring (Pearman

et al. 2008). Any variable not included in the model, for example biotic interactions or dispersal, is

assumed to either be non-limiting or to correlate with training variables (Godsoe & Harmon 2012).

During invasions these assumptions are often violated (Elith et al. 2010) and so using SDMs in this

context is inherently risky (Mesgaran et al. 2014). It should be noted that some SDMs explicitly

include biotic interactions or dispersal [e.g.Bateman et al. (2012); Quinn et al. (2014)], and although

this study focusses on climate-only SDMs the methods could also be applied to more complex models.

The accuracy of SDM projections is commonly assessed through cross-validation (Wenger & Olden

2012), whereby a random or otherwise-chosen subset of occurrence records are held back from each

model run and used for testing. While this is convenient because the model can still use all data for

training, cross-validation often gives an inflated measure of accuracy (Hijmans 2012). Independent

validation of SDM results is generally considered to be superior (Dormann et al. 2012), ideally using

independent survey data that is not spatially auto-correlated with training data (Araújo et al. 2005).

This is rare in practice, as presence/absence survey data can be difficult to obtain (Jeschke & Strayer

2008), and if the aim is to produce informative projections it may be beneficial to use all available

geographic regions for training, rather than handicap the SDM by denying it crucial information

(Broennimann & Guisan 2008). Importantly, even independent validation generally requires

information on where the species does not occur (absence data) in addition to presence locations,

potentially rewarding over-fitted models (Rodda et al. 2011).

For model validation, known presences and absences are usually compared to projected suitable and

unsuitable areas using confusion matrices and their derived metrics such as sensitivity and specificity

(Allouche et al. 2006), or to continuous model scores using AUC (Fielding & Bell 1997). These

metrics are commonly used in medicine to assess how well a clinical test detects a condition or disease

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in patients (Zweig & Campbell 1993). Applying the same logic to SDMs, each patient becomes a grid

cell in the landscape, each patient’s health the presence or absence of the species, and each clinical test

result is represented by the SDM score for the grid cell. Crucially, clinical tests aim to detect whether a

patient currently has a condition, not predict whether a patient could potentially fall ill. Yet confusion

matrices are often used to evaluate SDMs that aim not to project where invasive species currently are,

but where they might occur in the future. For example, projections of species’ climatic limits are

assessed against how well they predict whether grid cells are currently occupied or not. Logically, the

best possible model is then one that predicts suitability only where the species is already known to be,

and over-fitted models are likely to be rewarded. False absences (i.e. the SDM predicts climatic

unsuitability but the species is present) are good indicators of an unreliable model because if the

species is present the environment is probably suitable. However, false absences can also be caused by

sink populations, microhabitat and geo-referencing errors (Márcia Barbosa et al. 2013). Conversely,

false presences (i.e. SDM predicts suitability but the species is absent) are entirely ambiguous as a

species can be absent for many reasons, only one of which is environmental unsuitability. Reasons for

a species being absent from suitable environments include geographic barriers, biotic interactions,

dispersal patterns, non-climatic limitation, or it may simply not be detected (Lobo et al. 2010).

Modelling invasions is particularly problematic, because typically the species is assumed to be

expanding in its distribution (Elith et al. 2010) and there is no quantitative way to distinguish model

error from climatically suitable, yet-to-be colonized, habitat. Despite these apparent contradictions,

there are few examples of validating SDMs using anything other than distribution data.

Instead of distribution data, a better test of SDM performance is to compare projections with “bottom-

up” approaches, for example, plant performance data, population models or the physiological

requirements of the species (Kearney & Porter 2009). It might intuitively seem that if such data were

available, such as if there was sufficient knowledge of physiological requirements to build a

mechanistic model, it would be better to use bottom-up approaches to predict the species’ potential

distribution. Bottom-up approaches have been successfully applied to predicting species’ distributions

(Kearney & Porter 2004; Buckley 2008), but it is data-intensive and requires spatial projections of all

relevant driving variables. Small errors and uncertainties are compounded with increasing model

complexity, and as a result, bottom-up projections are not necessarily more accurate than top-down

approaches (correlative SDMs). Consequently, the method should be chosen according to the aims of

the study (Buckley et al. 2010). Some authors have combined bottom-up and top-down approaches to

produce more detailed or dynamic projections, albeit most commonly using climatic SDMs combined

with non-climatic metapopulation models (Anderson et al. 2009; Franklin et al. 2014). While such

“hybrid” models can improve species’ range forecasts and provide more detailed projections (Brook et

al. 2009), they assume that both the top-down and bottom-up components are accurate. Errors in the

underlying SDM projections will transfer to the hybrid projections, and Conlisk et al. (2013) show that

the SDM is the largest source of uncertainty in hybrid models. While this does not discount the

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usefulness of hybrid models, it is clear that there is still progress to be made in evaluating and

improving SDM outputs, which is the focus of this study.

Alternatively, Kearney and Porter (2009) suggest using bottom-up approaches to define areas of

unsuitability, against which SDMs could be validated and refined. This is distinct from validation

using pseudo-absences [locations where the species is thought to be absent due to lack of records,

though more complex pseudo-absence selection techniques exist e.g. Senay et al. (2013)] and true

absences (where the species is known to be absent through surveys). To distinguish the methods

presented here from pseudo-or true absences, I refer hereafter to fundamental absences, i.e. where

evidence suggests that locations are outside of the fundamental niche of the species, where abiotic

factors will prevent survival. Using fundamental absences to test SDM performance would give better

insight into model accuracy but few studies have taken such an approach. Sheppard et al. (2014)

compared SDM projections of climatic suitability for three non-native plants in New Zealand to

performance in field trials, but unsuitability was not explicitly defined, and the results were not used to

improve the model. Pattison and Mack (2008) used a similar method, correlating CLIMEX scores for

Triadica sebifera (L.) Small in the USA with performance of seeds and young plants, and Aragón et

al. (2010) used known physiological thresholds to validate model projections of Diabrotica virgifera

J. L. LeConte in Europe. Morin and Thuiller (2009) predicted the distributions of 15 tree species using

population models and SDMs, but it was a comparative study rather than a critical evaluation.

In this chapter, I demonstrate a novel method of validating and improving SDM projections in a

scenario where it is unrealistic to develop landscape-scale simulations using a bottom-up approach. In

Chapter 2, BIOCLIM (Nix 1986) was used to project suitable habitat in New Zealand for Aeonium

arboreum, A. haworthii and Cotyledon orbiculata, based on their global distributions, climate and

selected non-climatic factors. In recent years, BIOCLIM has declined in use and is often reported to

perform poorly in comparison to other models, but I determined it was the most appropriate tool for

modelling the three particular study species. In previous assessments of BIOCLIM, its performance

was assessed using occurrence data (Elith et al. 2006; Hernandez et al. 2006; Wisz et al. 2008). The

rectilinear envelope used by BIOCLIM will inevitably result in some over-prediction, but it is unclear

to what degree its reportedly poor performance is a consequence of it being less prone to overfitting

than more complex models. To test the accuracy of the SDM projections of the study species, I

develop a climate-driven integral projection model (IPM) of population growth using existing

performance data collected from Banks Peninsula, New Zealand (Chapter 3 and Chapter 4), and then

test the IPM against independent occurrence data. Whereas most population modelling efforts aim to

predict the growth of real populations of species, I aimed instead to identify where hypothetical

populations could self-sustain. Population growth was predicted in the steady state and transformed

into fundamental presences and absences, to identify where climate could support self-sustaining

populations assuming otherwise ideal non-climatic conditions. Existing BIOCLIM projections of

climatic suitability in the region of interest were tested against the fundamental presence/absence data,

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and SDM projections were then refined to remove as much prediction error as possible. The principles

of this method have been suggested by Kearney and Porter (2009), but to my knowledge have not been

previously demonstrated.

5.2.1 Aims

1. Combine existing linear regressions of climate-dependent mortality, growth, germination and

fecundity of the study species into a population model that predicts whether climate is

amenable to self-sustaining populations on Banks Peninsula.

2. Validate existing BIOCLIM projections of climatic suitability on Banks Peninsula against

projected population growth.

3. Improve BIOCLIM projections to more closely match population model predictions, and

improve maps of climatic suitability on Banks Peninsula for the study species.

5.3 Methods

5.3.1 Study species

This study builds on previous research on three succulent perennials in the Crassulaceae family;

Aeonium arboreum, A. haworthii, and Cotyledon orbiculata. Their potential distributions in New

Zealand are likely to be climate limited due to the comparatively hot and dry conditions of the native

ranges (Morocco, the Canary Islands and Southern Africa, respectively), and SDM projections (using

BIOCLIM) have indicated that the species’ distributions in New Zealand constitute a shift of the

realized niches (Chapter 2). Nevertheless, continued spread in New Zealand is apparent on cliffs,

roadsides and, in the case of C. orbiculata, grazing land, and the accuracy of SDM projections of

climatic suitability was uncertain. Field studies confirmed that growth rates, survival and germination

decline with increasingly cold and wet conditions in the study region (Chapter 3), but that plant size is

also an important predictor of mortality (Chapter 3) and fecundity (Chapter 4). Surveys of naturalized

populations in the study region indicated high mean seed output (approximately 26 000 seeds per

capita for A. arboreum, 5000 for A. haworthii and 192 000 for C. orbiculata). Propagule pressure from

naturalized populations is therefore likely to be high, and further spread appears likely. Although the

relationships between plant performance and climate were established in previous chapters, the

potential for new and existing populations to self-sustain across varying climatic conditions was not

clear, nor was how the species’ vital rates would interact to determine overall suitability under various

climatic conditions.

5.3.2 Study area

As in the two preceding chapters, I focus on the region of Banks Peninsula, New Zealand, where

previous field surveys and experiments on the study species were undertaken. Banks Peninsula

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comprises approximately 1150 km2 of hilly terrain extending from the coast south of Christchurch. All

three target species have established numerous populations on Banks Peninsula, mostly along the

northern coastline: the region contains 52% of all Aeonium occurrence records in New Zealand and

75% of C. orbiculata records. Because occurrence records on Banks Peninsula were used to train

BIOCLIM, testing the projections in the same region is not a fully independent test of model

performance. However, it was necessary to train the SDM using Banks Peninsula data because the

region represents the wettest extremes of the species’ realized niches. Testing projections on the

Peninsula was also valuable because, as a key area of invasion for all three species, accurate

projections of climatic limits are of interest to practitioners. Numerous training points in the test region

ensures that this is a “best-case” scenario of model performance. The results should, however, not be

extrapolated beyond the Peninsula because of the non-independence of test data.

The climate of the region is heterogeneous, with elevations ranging from 0 – 930 MASL, and

precipitation averaging from 600 - 1200 mm per year [(Hijmans et al. 2005), available from

http://www.worldclim.org]. Evidence suggests that this precipitation and elevation gradient extends

beyond the limits of climatic suitability for all three species (Chapter 3). The Peninsula contains much

suitable habitat for these succulent xerophytes, namely, volcanic cliffs and rock outcrops, roadside

cuttings, loess banks and sparse grassland (Webb et al. 1988). At the scale of SDM projections

(approximately 1 km2) there are few grid cells that do not contain suitable habitat, so it is assumed that

on Banks Peninsula invasion is limited primarily by climate.

5.3.3 Integral projection models

Generalized Linear Mixed Models (GLMMs) were previously fitted to field experiment and survey

data (Chapter 3 and Chapter 4) to describe climatic limitations to growth, mortality and fecundity

[collectively called vital rates (Tuljapurkar & Caswell 2012)] for the three target species. In all three

species, plant size (canopy volume) was a significant predictor of vital rates in addition to climate. The

GLMMs were integrated into a single population model per species. Integral projection models (IPMs)

were used, a technique developed by Easterling et al. (2000). The IPMs were used to predict whether

the species are likely to form self-sustaining populations under given climatic conditions.

Population growth (lambda; λ) of A. arboreum, A. haworthii and C. orbiculata was modelled using

IPMs because they offer distinct advantages over the more commonly-used matrix projection models

(MPMs) in situations involving continuous state variables. In this case, plant size (canopy volume)

was the state variable as it is a predictor of multiple vital rates. Although MPMs are useful when

modelling population growth over discrete time periods, they are suited to organisms that can be

divided into distinct classes based on age (Leslie matrices) or stage (Lefkovitch matrices). In MPMs,

each class has a unique probability of reproduction, mortality and transition to the next class. Where

no natural divisions in the life cycle exist, constraining the state variable (e.g. age, canopy volume)

into a matrix of few or arbitrary classes leads to over-inflated extinction risk, as MPMs ignore


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variation within classes (Fox & Kendall 2002). Conversely, with too many class divisions, the

calculations required to parametrize an MPM becomes impractical, with too few samples within each

class to predict vital rates (Ellner & Rees 2006). Integral projection models provide a solution to this

problem, and are well-described by Merow, Dahlgren, et al. (2014). All IPMs use the same principles

as MPMs, but instead of individually calculating transition probabilities across a small matrix, linear

regressions describing vital rates are integrated across a very large matrix of the state variable.

For clarity, it is necessary to qualitatively describe the structure and concepts behind IPMs before we

continue. As a first step, an n × n matrix of state variable classes (e.g. plant size as canopy volume) is

created by defining the maximum and minimum values. The number of cells in the matrix determines

the cell size (i.e. interval between classes), often set to 1000 × 1000, with each cell representing a class

of plant sizes. Next, three kernels describing fecundity, growth and mortality are defined. These

kernels combine multiple linear regressions of vital rates (e.g. probability of flowering, seeds per pod)

and are dependent on the state variable of the initial matrix (e.g. canopy volume), with or without

external driving variables (e.g. climate). Finally, the three kernels are integrated across the initial

matrix of size classes, to create an IPM matrix of transition probabilities between cells in each time

step. The locations within each cell where linear regressions are integrated are also defined by the user

(usually the mid-point of each cell). Fitting a climate-driven IPM therefore requires only a few linear

regressions describing vital rates as functions of the continuous state variable and climate.

5.3.4 Climate variables

Three IPMs were developed for predicting population growth (λ) at locations on Banks Peninsula, as a

function of climate. The key driving climate variables in the underlying GLMMs included annual frost

days (below 0 °C) and growing degree days (base 5 °C and 10 °C, hereafter referred to as GDD5 and

GDD10). These variables are not available as spatial layers, so it was not feasible to project the IPMs

across the entire Banks Peninsula. Instead, I ran the IPMs at point locations using temperature data

from existing weather stations, field surveys and experiments. At 71 field sites I had previously

recorded four-hourly temperature data (°C) using iButton™ data loggers, between December 2010 and

November 2012 (Chapter 3 and Chapter 4). In addition, I downloaded daily maximum and minimum

temperature from the 12 available weather stations between latitudes - 43.325 and - 43.900, and

longitudes 172.294 and 173.131 decimal degrees (WGS 1984). Data were obtained from the CliFlo

database [(National Institute of Water and Atmospheric Research 2014), http://cliflo.niwa.co.nz/].

Combining all temperature data from December 2010 – November 2012 provided 83 point locations

with the climate data necessary to run the IPM (Table D.1).

At each point location, frost days, GDD5 and GDD10 were calculated from recorded daily maximum

and minimum temperatures, and monthly solar radiation (KWh/m2) was modelled at the same

locations using the Solar Radiation tool in ArcMap 10.1 (Fu & Rich 1999; Environmental Systems

Research Institute 2011). Not all weather stations record both temperature and precipitation, and only

http://cliflo.niwa.co.nz/

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temperature was recorded at the 71 field sites. I therefore estimated monthly precipitation (mm) for

point locations without rainfall data, using the nearest neighbour station in the CliFlo database (14

stations total, Table D.1).

Time periods over which climate variables were summed (e.g. annual precipitation) were the same as

were used in the original GLMMs. In other words, July-December climate totals were used to drive

regressions in the fecundity kernels, December-June totals for survival kernels, and annual totals for

the growth kernels. Finally, I used the means of climate variables (e.g. annual frost days) over

December 2010 – November 2012 as the driving variables for the IPM at each point location. For

predictions to be useful, the two-year means (December 2010 – November 2012) should be

representative of longer-term averages at the sites. To test this assumption I compared the two-year

means to five, ten and twenty-year means at the 12 weather stations, using a paired t-test with alpha

levels adjusted using the Bonferroni correction. I then tested whether the trends recorded by data

loggers were comparable to those recorded at weather stations over the same period (December 2010 –

November 2012), by calculating mean correlation (r) between the residuals of the means of

temperatures recorded by data loggers versus the nearest weather station. Both daily maximum and

daily minimum temperatures were compared.

There were no significant differences in two, five, ten or twenty-year means of annual frost days at

any of the weather station sites (Figure D.1, Table D.2). There were significant differences in annual

GDD5 and GDD10, but between the two and five-year means only. Between December 2010 and

November 2012, data loggers recorded more extreme temperatures than weather stations. In particular,

maximum temperatures were higher (mean r of residuals = 0.54; Figure D.2). This is expected, as the

weather stations are mostly low elevation and/or coastal, while data loggers were in exposed locations.

Daily minimum temperatures were well correlated between data loggers and weather stations (mean r

of residuals = 0.85; Table D.3). In summary, there was good evidence that the two-year climate means

used in the IPMs were representative of longer-term trends.

5.3.5 IPM parameters

The IPMs were based on annual time steps, standard practice for long-lived perennial plants (Merow,

Smith, et al. 2014). The models were run over one time step using the mean climate variables,

beginning on 1st December and ended on 30

th November to align with field experiments and surveys,

where 1st December approximately marks the beginning of the flowering season for the species. Linear

regressions for the fecundity and mortality kernels were identical to those described in Chapter 3 and

Chapter 4, with random effects set to zero where applicable (Table 5.1).

Growth kernels were simpler than the regressions described in Chapter 3, because preliminary

attempts to introduce a “rapid growth stage” as observed in the first year of the field experiments

(Figure 3.4) led to unstable model behaviour. Instead, I fitted a model using a similar structure to the

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growth kernels in the R package IPMpack (Metcalf et al. 2013). Canopy volumes (L) of plants at

experimental sites in November 2011 and 2012 were used as the response variable “Volume t+1”.

Using stepwise backward selection, I fitted a GLMM with the random effects Site and Source,

identical to those used in Chapter 3. I fitted fixed effects of annual climate variables and canopy

volume (L) at previous time step (“Volume t”). Marginal R2 (Johnson 2014) of the growth models

were 0.42 for A. arboreum, 0.21 for A. haworthii and 0.22 for C. orbiculata.

Table 5.1 Linear regressions of vital rates of Aeonium arboreum (AA), A. haworthii (AH) and

Cotyledon orbiculata (CO), as used in IPMs. Parameters of each regression shown, and whether the

regression was fitted to experimental (Chapter 3) or survey (Chapter 4) data. Model coefficients are

available in Table S.1. Units are plant volume (L), elevation (MASL), precipitation (mm/year) Frost

days, GDD and precipitation were 2-year annual means for each variable.

Vital rate Species Parameters Source Thesis figure

P[Die] summer AA Volume + Elevation Experiment Figure 3.6

AH Volume + Elevation Experiment Figure 3.6

CO Volume Experiment Figure 3.6

P[Die] winter AA Volume + Cumulative Frost Days Experiment Figure 3.7

AH Volume + Cumulative Frost Days Experiment Figure 3.7

CO Volume + Cumulative Frost Days Experiment Figure 3.7

Volume t+1 AA Volume t + Elevation + Elevation2 Experiment Table S.1

AH Volume t + Elevation + Frost Experiment Table S.1

CO Volume t + Elevation + Elevation2 Experiment Table S.1

P[Flower] AA Volume + GDD10 Surveys Figure 4.2

AH Volume Surveys Figure 4.2

CO Volume + Solar Radiation Surveys Figure 4.2

Inflorescences

per plant

AA Constant Surveys Table S.1

AH Constant Surveys Table S.1

CO Volume Surveys Figure 4.3

Flowers per

inflorescence

AA Aspect Surveys Figure 4.4


CO Volume Surveys Figure 4.4

Seeds per pod AA Aspect + Pods + (Aspect*Pods) Surveys Figure 4.5


CO Constant Surveys Table S.1

Seedling success AA GDD5 + Frost Days + Precipitation Experiment Figure 3.3

AH Elevation Experiment Figure 3.3

CO Precipitation Experiment Figure 3.3

In linear regressions that contained aspect as a driving variable, I chose to predict vital rates for north-

facing aspects to represent favourable conditions for all species. Assuming that the majority of grid

cells on Banks Peninsula contain at least one north-facing slope, this mitigates the risk of under-

predicting potential ranges. Canopy volume (v) was normalised by log-standardizing against the

relevant original raw data (y) used in original linear regressions in Chapters 3 and 4, according to

equation 1. Constant values, the observed means across all survey sites between December 2010 –

November 2012, were used to describe inflorescences per plant in A. arboreum, all seed and flower

production in A. haworthii and seeds per pod in C. orbiculata. Constant mean values were used for

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Aeonium species where no strong relationships with plant volume or climate had been found during

field surveys. For C. orbiculata, constant seeds per pod were used to prevent extreme values when

extrapolating. In its native range, C. orbiculata var. dactylopsis produces on average 1585 ovules per

flower (Zietsman 1998), while the IPM predicted values of up to 15 890 seeds per pod. This was a

result of extrapolating the relationship to larger inflorescences than were actually sampled, hence

mean seeds per pod were used. The original regression for C. orbiculata is shown in equation 2, and

because aspect was a driving variable, I again used the mean number of seeds at north-facing sites.

The same regression was used to predict A. arboreum seeds per pod, but it did not lead to extreme

predictions for this species, as seeds per pod was less variable, and flowers per inflorescence was more

representative in the original dataset.

Log Standardized Canopy Volume = {ln [vi] - �̅� [ln (y)]}/{2s [ln (y)]} (1)

Seeds per Pod = Aspect + Pods per Inflorescence + (Aspect × Pods per Inflorescence) (2)

5.3.6 IPM structure

Each vital rate regression was incorporated into one of the three kernels of the IPM: survival, growth

or fecundity. For each of the 83 point locations, the kernels were integrated across the initial matrix of

size classes of canopy volume to create a survival vector (S), and growth (G) and fecundity (F)

matrices (see Figure D.3 for a simplified example of the model structure). The IPM matrix for each

location showing transition probability among size classes of canopy volume, is calculated by first

creating P, a growth and survival matrix (equation 3). Then, F is incorporated to make the IPM matrix

(K, equation 4). Though a vector of initial conditions is usually supplied, eigenvectors and lambda (λ)

were calculated from transition probabilities with no initial conditions, equivalent to population

growth in the steady state. The steady state was used in order to answer whether a hypothetical

population could self-sustain at point locations, including at current absences, without biasing the

model with arbitrary initial conditions for species with unknown dispersal capabilities. Lambda is

calculated using the eigen function in R’s base package, as lambda=Re(eigen(K)$values[1]). This

function calculates the eigenvalues for the matrix and returns them as a vector sorted in decreasing

order, where the dominant (largest) eigenvalue equals lambda.

P = G × S (3)

K = P + F. (4)

The initial matrices of size classes were rescaled from the original state variable canopy volume (L),

because it was difficult to see model behaviour in small plants. I instead used the state variable

3√(Volume × 10

3), approximately equivalent to plant height. This did not alter model predictions as

plant height was rescaled to canopy volume before input into the vital rate regressions. I defined the

initial matrix as a 1000 × 1000 cell matrix between 2 cm and 55 cm height, based on observed sizes of

seedlings and mature plants during surveys. Kernel functions were integrated using the simplest

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option, the midpoint rule (Merow, Dahlgren, et al. 2014). In order to run the IPM on an annual time

step, the survival kernel incorporated summer and winter mortality (equation 5). Growth kernels

contained the linear regressions described in Table 5.1, which predict mean canopy volume at time

t+1 based on volume at time t, plus climate. The distribution around the mean was Gaussian with a

standard deviation of 5 cm, equivalent to the residual variances of the fitted growth models.

Annual Survival = (1-P[Die] winter) × (1-P[Die] summer) (5)

The fecundity kernel was driven by probability of reproduction P[Reproduce] and per capita seed

output. Probability of reproduction was defined according to equation 6. Establishment probability

(P[Establish]) is often incorporated into IPMs as a constant, the probability of a seed landing in a

favourable location for germination (Metcalf et al. 2013; Merow, Dahlgren, et al. 2014). I set

establishment to P[1] to model population growth under optimum conditions. Seedling success is the

probability of germination and subsequent annual seedling survival (the models derived from field

experiments, Chapter 3). If the IPMs for the three species were to be used for dynamic or temporally

explicit projections, they should include a discrete seedling stage akin to a seed bank [see Ellner and

Rees (2006)]. As predictions were static, I simplified flowering, germination and seedling survival to

occur in the same time step with no seedling bank. Per capita seed output was calculated according to

equation 7. The final fecundity kernel combines reproduction and seed output (equation 8), and

predicts how many seeds per capita develop, germinate and survive to become seedlings. The resulting

seedlings enter the IPM matrix as a normal distribution of individuals centred on the mean recruitment

size, set to 2 cm height with a standard deviation of 1 cm.

P[Reproduce] = P[Flower] × P[Establish] × P[Seedling Success] (6)

Seed Output = Inflorescences per Plant × Flowers per Inflorescence × Seeds per Pod. (7)

Fecundity = P[Reproduce] × Seed Output (8)

5.3.7 Verification of IPMs

Predictions of the IPMs were assessed against true presences of the target species, and were

considered reliable on the condition that λ was consistently > 1 at presence locations, in other words if

positive population growth was predicted. Predicted λ at true absence locations was not used to test the

IPMs because true absences are ambiguous; species may be absent from a location for a number of

reasons not necessarily related to climate. Additionally, the species are still spreading in the region, so

“false presences” are expected. However, both predicted λ at true presence and absence locations were

used to assess the proportion of currently unoccupied sites with potential for invasion. Predictions

were compared between species by calculating the Jaccard similarity index of λ scores, converted to

fundamental presence/absence using a threshold of 1. Models were checked for spurious or

biologically unrealistic behaviour by plotting the IPM (K) and growth (G) matrices, and the stable size

distributions (the right eigenvectors). I checked and corrected for eviction, where individuals are

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dropped from the matrix upon falling outside of the minimum or maximum size classes [see Williams

et al. (2012)], by plotting the survival function and column sums of the growth and survival (P)

matrix. Predicted P and K matrices, and stable size distributions at the 5th and 95

th percentile locations

when ranked by λ (i.e. “poor” and “good” sites), are shown in Figure D.4, Figure D.5 and Figure D.6.

To investigate which driving variables and plant size classes had most effect on λ, I ran perturbation

and elasticity analyses on predictions at the 5th and 95

th percentile locations. As sensitivities and

elasticities were highly similar, only elasticity is presented. Elasticity measures the change in λ

proportional to the change in each variable, thus accounting for the different scales (e.g. plant height

vs. probabilistic regressions). The elasticity analysis is part of standard IPM code (Metcalf et al. 2013;

Merow, Dahlgren, et al. 2014), and derives elasticity from the left and right eigenvectors of the matrix,

indicating size classes that have most influence on λ. The perturbation analysis measures the relative

influence of driving variables on λ (Caswell 2000), by changing each parameter in the IPM by a delta

(Δ) value of 0.0001 (equation 9).

Elasticity = (new λ – original λ)/(original λ – Δ) (9)

5.3.8 Validation of BIOCLIM projections

The 83 predicted λ values for each species at each point location were used to validate BIOCLIM

projections for Banks Peninsula (Chapter 2.4.3), on the assumption that the IPM represents a best

estimate of true climatic suitability for each species. This assumption is defensible on the basis that all

linear regressions in the IPMs are derived from high-power field data in the same region, with minimal

extrapolation or additional assumptions, and the IPM predictions were shown to be reasonable before

carrying out further analysis. I transformed BIOCLIM and IPM projections into binary projections of

suitability. BIOCLIM has a natural threshold; scores of 0 indicate that climatic conditions are outside

of the “envelope” defined by presence data and are presumably unsuitable. For the IPM scores, I used

1 as the threshold, where λ < 1 indicate that populations are not predicted to be self-sustaining due to

negative population growth rate in the steady state. I resampled all IPM points onto a 30 arc-second

raster grid aligned with BIOCLIM projections, taking the mean λ when multiple points fell within a

grid cell. I then calculated confusion matrices to evaluate the performance of BIOCLIM (“prediction”)

against the 83 IPM fundamental presences and absences (“reality”). For comparison with conventional

validation techniques, I calculated confusion matrices using 5-fold cross-validated presence/absence

data for Banks Peninsula (occurrence data shown in Appendix C).

The most common metrics calculated from confusion matrices are sensitivity and specificity [see

Allouche et al. (2006) for a comprehensive explanation of these]. Sensitivity measures the proportion

of presences correctly identified by the model, while specificity does the same for absences. These

metrics may be misleading depending on the structure of the occurrence data. For example, with a

50:50 split of true presence and absence points within a predicted absence area (i.e. model likely to be

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under-predicting) sensitivity and specificity could equal 75% (a “good” model) if there are three times

as many presence points as absence points overall. Instead, Márcia Barbosa et al. (2013) propose the

over- and under-prediction rates (OPR and UPR respectively). These metrics are the proportions of all

predicted absences that contain true presences (OPR), and predicted presences that contain true

absences (UPR). From the confusion matrices I calculated sensitivity, specificity, UPR, and OPR of

BIOCLIM projections. To test whether true presences were likely to have high BIOCLIM scores, and

vice versa, I calculated area under the ROC curve (AUC). A common, if somewhat arbitrary rule-of-

thumb is that models are useful only if AUC > 0.7 (Greiner et al. 2000).

5.3.9 Improving BIOCLIM projections

The final aim was to improve BIOCLIM projections for Banks Peninsula. Assuming that the

projections would not be perfect, there are two possibilities; that overall, BIOCLIM under-predicts

climatic suitability on Banks Peninsula, or it over-predicts. If results showed BIOCLIM to be under-

predicting, I aimed to input false absence locations (where λ > 1 but BIOCLIM = 0) back into the

original SDMs as additional training presences, to extend projected range limits. This assumes that

BIOCLIM under-predicts due to niche expansion in New Zealand and non-equilibrium distribution. In

the case of over-prediction, I aimed to test whether presences and absences, as defined by the IPM,

had significantly different BIOCLIM scores. This assumes that low BIOCLIM scores (i.e. the outer

edges of the climatic envelope) represent marginal conditions that cannot support self-sustaining

populations, and will not remove any over-prediction in the “core” envelope. To test whether the mean

BIOCLIM scores were significantly different between fundamental presences and absences, I would

run 1000 - fold bootstraps of BIOCLIM scores at fundamental presence and absence locations, plot the

distributions, and perform a single-factor ANOVA of the BIOCLIM scores of the two groups. If

fundamental presences and absences had significantly different scores to each other, I would re-

calculate the confusion matrices iteratively, raising the BIOCLIM threshold by 0.001 on each run

between 0 and the maximum score. A new BIOCLIM threshold would then be chosen as the value that

best distinguished fundamental presences from fundamental absences. For the recalculation of

confusion matrices, fundamental and true presences were pooled to minimize the risk of raising the

threshold too high and under-predicting suitable climate. The new threshold was to be the value with

the lowest under prediction rate (UPR, described in section 5.3.8) within 0.01 of the maximum True

Skill Statistic (TSS, equal to sensitivity plus specificity, minus 1). Maximising TSS would remove as

much over-prediction from the BIOCLIM projections as possible, while keeping UPR as low would

minimize risk of raising the threshold too high and removing truly suitable climate.

5.4 Results

5.4.1 IPM predictions

Across the 83 point locations used for IPM projections, lambda (λ) ranged from 0.64 - 7.43 for

A. arboreum, 0.002 - 1.54 for A. haworthii, and 0.04 - 7.40 for C. orbiculata. The IPM predicted

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Aeonium haworthii to have the lowest maximum λ of all species, and ranked plots of λ revealed an

asymptotic curve. This is because seed output for A. haworthii was the lowest of all three species,

producing fewer flowers and fewer seeds per flower. Furthermore, while probability of flowering

increases with size in A. haworthii models, reproductive output is constant. Consequently, predicted

reproductive output of A. haworthii in the steady state cannot increase once P[Flower]→1. Across the

83 sites, λ correlated positively but weakly among species (between the Aeonium species r = 0.63,

between C. orbiculata and A. arboreum 0.50, and between C. orbiculata and A. haworthii 0.59).

Converting λ to fundamental presence/absence revealed that, among species, there was a high degree

of overlap in whether locations were classified as suitable or unsuitable (Jaccard Similarity = 0.87

between Aeonium species, 0.63 between C. orbiculata and both Aeonium species). All sites that were

dissimilar between C. orbiculata and Aeonium species were predicted as suitable for the former, and

unsuitable for the latter.

The IPMs predicted that at colder sites, growth rates are low, and as a result, mortality increases as

individuals die back continuously (Figure D.5). As reproduction is size-dependent, low growth also

results in little to no recruitment at unfavourable locations. Irrespective of plant size, survival is low at

unfavourable sites, compounding the effect of low growth rates (Figure D.6). The IPMs predicted

λ > 1 at the majority of known presence locations for all three species (Table 5.2). I investigated the

remaining false absences (where λ < 1), and found three sources of error: cultivated populations,

spatial scale, and possible marginal populations. With respect to cultivated populations, four locations

(Birdling’s Flat, Lincoln, Leeston, and “CKSE” in Central Christchurch) were predicted as unsuitable

for at least one species. Though the species are present, they are single plants in outdoor gardens.

Spatial scale was an issue for the IPM location “Greenwood Park 4” where λ = 0.44. Cotyledon

orbiculata is present within the same grid cell as the IPM location, but approximately 100 m lower,

and in small numbers. Finally, while C. orbiculata is present at both locations at Okains Bay, at one

location the IPM predicted λ = 0.95. This particular location contains a small population with

relatively poor performance (Figure C.6), and is potentially a marginal population, although other

sources of error cannot be discounted. Overall, the majority of true presences in all three species were

predicted to be self-sustaining. As described previously, false presences are not considered sources of

error as the species are not at equilibrium.

Table 5.2 Verification of integral projection models of Aeonium arboreum, A. haworthii and

Cotyledon orbiculata, run at 83 point locations on Banks Peninsula. Sites divided according to

species’ current presence or absence. Sites with predicted population growth (λ) >1 were classified as

suitable, <1 were classified unsuitable.

Species present Species absent

IPM suitable IPM unsuitable IPM suitable IPM unsuitable

A. arboreum 26 1 16 40

A. haworthii 29 2 13 39

C. orbiculata 35 4 32 12

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Table 5.3 Elasticity values of IPM parameters. Perturbation analyses conducted for Aeonium arboreum, A. haworthii and Cotyledon orbiculata at favourable sites

(upper 95th percentile of λ) and unfavourable sites (lower 95

th percentile of λ), with the three highest elasticities highlighted for each species.

Stage Parameter Favourable site Unfavourable site

A. arboreum A. haworthii C. orbiculata A. arboreum A. haworthii C. orbiculata

Summer survival Intercept - 0.02 - 0.02 - 0.42 - 0.06 - 0.68 - 0.04

Volume - 0.01 - 0.01 - 0.30 - 0.02 - 0.19 - 0.02

Elevation - 0.01 - 0.01

- 0.02 - 0.61

Winter survival Intercept 3.6 × 10-6

3.3 × 10-6

- 1.2 × 10-7

- 0.53 - 2.48 - 2.09

Volume - 8.7 × 10-6

3.3 × 10-6

- 1.2 × 10-7

- 0.45 - 1.12 - 0.36

Frost 1.6 × 10-6

3.4 × 10-6

- 1.2 × 10-7

- 0.76 - 4.88 - 2.22

Growth Intercept - 0.50 - 0.11 - 0.80 - 0.06 - 0.93 - 1.37

Elevation - 0.16 - 0.06 - 0.13 - 0.02 - 0.65 - 0.29

Elevation2 - 0.30 - 0.50 - 0.03 - 1.40

Frost - 0.07 - 0.51

Previous size - 0.13 - 0.12 - 0.06 - 0.26 - 2.53 - 1.73

SD - 0.20 - 0.14 - 0.59 - 0.18 - 2.52 - 1.64

P[Flower] Intercept - 1.53 - 0.95 - 0.06 - 5.9 × 10-6

-4.2 × 10-5

- 1.1 × 10-5

Volume - 0.41 - 0.19 - 4.5 × 10-3

- 5.2 × 10-6

-4.2 × 10-5

- 1.1 × 10-5

GDD10 - 0.86 - 5.7 × 10-6

Radiation - 0.01 - 1.1 × 10-5

Inflorescences Intercept - 0.38 - 0.20 - 0.50 - 5.4 × 10-6

-4.2 × 10-5

- 1.1 × 10-5

Volume - 0.28 - 1.1 × 10-5

Flowers Intercept - 0.38 - 1.09 - 1.74 - 5.4 × 10-6

-4.2 × 10-5

- 1.0 × 10-5

Volume - 0.45 - 1.1 × 10-5

Seeds Intercept - 1.00 - 0.57 - 0.43 - 5.2 × 10-6

-4.2 × 10-5

- 1.1 × 10-5

Flowers - 0.01 - 5.5 × 10-6

Germination Intercept - 1.51 -1.60 - 4.02 - 6.3 × 10-6

-4.2 × 10-5

- 1.2 × 10-5

GDD5 - 0.81 - 5.5 × 10-6

Frost - 0.54 - 5.5 × 10-6

Precipitation - 0.16 - 1.73 - 5.5 × 10-6

- 1.1 × 10-5

Elevation - 0.74 -4.2 × 10-5

Recruit size Mean - 0.61 - 0.36 - 0.74 - 5.2 × 10-6

-4.2 × 10-5

- 1.1 × 10-5

SD - 0.38 1.1 × 10-3

- 0.06 - 5.4 × 10-6

-4.2 × 10-5

- 1.1 × 10-5

Establishment P[Establish] - 0.38 - 0.22 - 0.43 - 5.4 × 10-6

-4.2 × 10-5

- 1.1 × 10-5

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5.4.2 Perturbation analyses

Elasticity plots of IPM matrices revealed that at favourable sites, λ was most affected by changes in

the growth rates of small plants (i.e. less than 30 cm height, Figure D.7). When plants are small, minor

increases in growth rates facilitates reproduction, and population growth increases rapidly. At

unfavourable sites, changes to growth in medium-to-large plants had the most effect, as increases in

growth at this stage reduces net die-back, allowing ongoing winter survival. Perturbation of individual

parameters resulted in similar patterns to the matrix plots, where λ at favourable sites was most

affected by parameters related to reproduction (Table 5.3). At unfavourable sites, parameters related to

growth and survival affected λ most. Additionally, λ tended to be more sensitive to regression

intercepts than to climate or volume parameters, particularly at favourable sites.

5.4.3 Validation of BIOCLIM projections

Predicted λ tended to be highest at low elevations or near coastlines for all three species. Notable

exceptions were locations on the Canterbury plains, where IPMs of all three species commonly

predicted λ < 1. Despite the low elevations, the plains more frequently experience sub-zero

temperatures than sites on Banks Peninsula (up to 63 mean annual frost days at Christchurch Airport,

while Banks Peninsula had maximum of 7). In the IPMs, frost days limit winter survival for all three

species, growth for A. haworthii, and germination for A. arboreum. For both Aeonium species, all grid

cells classified as unsuitable by BIOCLIM were predicted by the IPMs to be fundamental absences

(Figure 5.1). In other words, UPR of BIOCLIM = 0. By extension, grid cells containing fundamental

presences were projected as suitable by BIOCLIM in 100% of instances (sensitivity = 1). Sensitivity

was also 1 for C. orbiculata, but the UPR could not be assessed because BIOCLIM predicted no

unsuitable grid cells. However, in all three species a number of fundamental absences were incorrectly

classified as suitable by BIOCLIM (i.e. specificity was low, between 0 – 0.4). As a proportion of all

BIOCLIM cells predicted as suitable, 10 - 30% contained fundamental absences (OPR = 0.1 - 0.3).

The confusion matrices for BIOCLIM projections were repeated using occurrence data (Table 5.5),

and despite the over-prediction of BIOCLIM, it performed better than traditional cross-validation

techniques would have suggested. For example, cross-validation indicated misleadingly high over

prediction rates (OPR) of 0.95 for both Aeonium species, and 0.89 for C. orbiculata. This was due to a

large number of currently unoccupied grid cells along the coastlines, where BIOCLIM was penalized

for projecting suitability, despite it being likely to be true.

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Figure 5.1 Graphical representation of confusion matrices validating BIOCLIM against IPM

predictions. Points show BIOCLIM score vs. λ at each location where IPMs were run, for a) Aeonium

arboreum, b) A. haworthii and c) Cotyledon orbiculata. Lines indicate where BIOCLIM > 0 (projected

suitable by BIOCLIM) and λ = 1 (threshold for suitable/unsuitable in IPM). Because BIOCLIM scores

all unsuitable sites as 0, lines are drawn at the lowest BIOCLIM score on Banks Peninsula.

5.4.4 Can BIOCLIM distinguish fundamental presences from absences?

In all three species, 100% of fundamental presences were correctly predicted by BIOCLIM, and areas

projected as unsuitable by BIOCLIM are unlikely to sustain populations of the species. However,

BIOCLIM clearly over-predicts both at the range limits (where BIOCLIM scores are low but > 0) and

within the “core” climate (where BIOCLIM scores are high). Despite this over-prediction, AUCs were

sufficient for the model to be classified as useful; 0.70 ± 0.13 for A. arboreum, 0.77 ± 0.12 for

A. haworthii and 0.71 ± 0.20 for C. orbiculata. Therefore, while BIOCLIM ranked sites well in order

of suitability, the threshold of 0 for defining unsuitability was too low. The ANOVA results (Table

5.4), confirmed that BIOCLIM scores at fundamental presence and absence locations were

significantly different, with large F-ratios (especially in the case of A. haworthii). Bootstrapped

distributions of mean BIOCLIM scores also revealed little overlap, indicating that true population

means are likely to be significantly different (Figure D.8).

Table 5.4 Single factor ANOVA comparing BIOCLIM scores at fundamental presence and absence

locations for Aeonium arboreum, A. haworthii and Cotyledon orbiculata. Fundamental presences and

absences distinguished by the threshold of λ = 1 for IPM predictions.

Species Factor DF SS MS F

A. arboreum Binary λ 1 0.13 0.13 7.71 **

Residuals 78 1.33 0.02

A. haworthii Binary λ 1 0.29 0.29 16.18 ***

Residuals 81 1.46 0.02

C. orbiculata Binary λ 1 0.04 0.04 4.9 *

Residuals 133 1.19 0.01

A B C

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Figure 5.2a) New Zealand and b) Banks Peninsula BIOCLIM projections for Aeonium arboreum. Grey cells are projected as unsuitable by BIOCLIM. Predicted λ

(IPM) for each species shown as graduated red points at each IPM location, black points represent λ < 1 (unsuitable). Shaded relief shown on Banks Peninsula.

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Figure 5.3a) New Zealand and b) Banks Peninsula BIOCLIM projections for Aeonium haworthii. Grey cells are projected as unsuitable by BIOCLIM. Predicted λ


109

Figure 5.4a) New Zealand and b) Banks Peninsula BIOCLIM projections for Cotyledon orbiculata. Grey cells are projected as unsuitable by BIOCLIM. Predicted λ


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5.4.5 Improving BIOCLIM projections for Banks Peninsula

Following the results of the previous analyses, I constrained BIOCLIM projections on Banks

Peninsula by raising the threshold for unsuitability above the default of 0, to refine projections and

remove as much over-prediction as possible. Confusion matrices were iteratively re-calculated (Figure

D.9) by increasing thresholds as described in Section 5.3.9, maximising TSS while minimizing UPR.

From this analysis the following new thresholds were chosen; 0.036 for A. arboreum and A. haworthii,

and 0.046 for C. orbiculata. Projections for Banks Peninsula were then re-mapped as grid cells

originally classified as unsuitable by BIOCLIM (assumed to be truly unsuitable), cells with BIOCLIM

scores below the new thresholds (likely to be unsuitable), and those above the threshold (likely to be

suitable, Figure 5.5). The new thresholds improved BIOCLIM performance for all three species by

removing some over-prediction while retaining model sensitivity (Table 5.5). The updated projections

are similar to the original BIOCLIM projections for both Aeonium species, removing only the highest

elevation grid cells. However, suitable area for A. arboreum dropped by 22% after projection

refinement, leading to the smallest predicted range of all three species. Fewest grid cells were removed

for A. haworthii, resulting in the largest predicted suitable area of the three species (70% of Banks

Peninsula). Refining projections was most effective in the case of C. orbiculata, excluding much of

the wetter southern part of the Peninsula as “likely unsuitable”, whereas original BIOCLIM models

were unable to exclude any grid cells as potential invasion sites. For C. orbiculata, final models

indicate that climate is likely to be suitable in 63% of grid cells on the Peninsula.

Table 5.5 Sensitivity, specificity, under prediction rate (UPR) and over prediction rate (OPR), and

projected suitable area (PSA, %), for Aeonium arboreum, A. haworthii and Cotyledon orbiculata. All

metrics calculated for Banks Peninsula only. Original models (unrefined BIOCLIM projections)

validated against IPM predictions. The same metrics are shown for refined BIOCLIM projections,

calculated against IPM predictions and true presences.

Metric A. arboreum A. haworthii C. orbiculata

Cross-

Validated Original Refined

Cross-


Cross-


Sensitivity 1 1 0.94 1 1 0.96 1 1 0.98

Specificity 0.26 0.41 0.47 0.22 0.33 0.47 0 0 0.54

UPR 0 0 0.17 0 0 0.13 N/A N/A 0.30

OPR 0.95 0.28 0.27 0.95 0.27 0.24 0.89 0.10 0.05

PSA 73% 73% 51% 77% 77% 70% 100% 100% 63%

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Figure 5.5 Refined BIOCLIM projections for b) Aeonium arboreum, c) A. haworthii and c) Cotyledon orbiculata on Banks Peninsula, with shaded relief, and extent

indicator (a). Categories are: predicted unsuitable by BIOCLIM (blue, unsuitable), predicted suitable by BIOCLIM but below IPM-based threshold (yellow, likely

unsuitable), and predicted suitable by BIOCLIM and above the IPM-based threshold (red, likely suitable).

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5.5 Discussion

5.5.1 Accuracy of IPM and BIOCLIM projections

The IPM consistently predicted self-sustaining populations at the majority of true presence locations.

At the few locations where predicted λ was less than 1, existing populations were small, cultivated or

at lower elevations than the IPM point location. Because IPM performance was not assessed against

true absences on Banks Peninsula, over-prediction of range limits by the IPM cannot be discounted. In

fact, it is likely that running the IPM in the steady state, and as a closed system where all seeds have a

chance to germinate, that λ values are optimistic. For these wind-dispersed species, seed rain may be

lost from populations depending on elevation, barriers, shelter and wind direction (Okubo & Levin

1989). Further limitations are discussed in detail in Section 5.5.3. Despite potential over prediction,

the regressions that underpin the IPM are derived from large-scale experiment and field data in the

region of interest, and have a high degree of explanatory power (Section 3.4). The aim was not to

predict actual rates of population growth in existing populations, but to provide meaningful delineation

of climatic unsuitability assuming otherwise favourable conditions. The IPMs therefore appear

sufficient to predict fundamental absences, with the caveat that they may still slightly over-predict

range limits. It is worth noting that over-prediction is preferable to under-prediction in a pest risk

context (Jiménez-Valverde et al. 2011). Predictions also align well with the known biology of the

three species: they are thought to be frost sensitive (Vogan 2003), are likely to be close to their

climatic limits on Banks Peninsula, and behaviour of the IPMs is consistent with the interpretation of

the field experiment data (Section 3.4.4).

Validation of BIOCLIM against IPM predictions revealed unexpected behaviour in the SDM. It has

previously been reported that BIOCLIM over-predicts suitable habitat (Elith et al. 2006; Hernandez et

al. 2006; Wisz et al. 2008). Over-prediction occurs is because BIOCLIM fits a rectilinear envelope in

climate space around all presence locations, with no interactions between climate variables, instead of

building complex response curves to the variables (Booth et al. 2014). The simplicity of BIOCLIM

was the reason it was used to model these species (Section 2.3.5), but some over-prediction was

inevitable. On the other hand, BIOCLIM classifies as unsuitable any grid cell with one or more

climate variable outside the bounding box of the envelope, whereas more complex models can

extrapolate into novel climates. As a result, over-prediction within the “core” envelope, but under-

prediction of range limits (i.e. the boundaries of the envelope) was expected, especially because there

is evidence of a shift in the species’ realized niches in New Zealand (Section 2.4.1). Surprisingly,

BIOCLIM over-predicted suitable climate both within the envelope (as demonstrated by the high

projected suitability of the Canterbury Plains), as well as at range limits (IPMs predicted fundamental

absences at lower elevations than BIOCLIM projected unsuitability). An important point is that

BIOCLIM’s performance was better than indicated by the standard cross-validation using

presence/absence data, because λ was positive at a number of locations where the species are not yet

present. Most studies identifying poor performance of BIOCLIM have done so using occurrence data

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(Hernandez et al. 2006; Wisz et al. 2008; Smith et al. 2013), which as demonstrated, may be

misleading. Despite its over-prediction, BIOCLIM’s projections were useful. Ranking sites by

BIOCLIM scores aligned relatively well with λ, as demonstrated by the AUC scores (0.7 - 0.76) and

Figure 5.1. Sensitivity was also perfect (100%) in all cases, and therefore where BIOCLIM projects

unsuitability, there is good evidence that it can be trusted. The agreement between the two models also

allowed BIOCLIM projections to be refined to more accurately reflect climatic range limits.

5.5.2 Why did BIOCLIM over-predict suitable climate?

Many studies have tested relative performance of SDMs (Elith et al. 2006; Hernandez et al. 2006;

Aguirre-Gutiérrez et al. 2013), but it is difficult to infer the cause of poor model performance when

they are evaluated against occurrence data. Non-climatic limitation and complex model algorithms

may cloud sources of model error, and distinguishing whether the model is capturing real biological

processes or is over-fitting is not straightforward. In this study, the use of fundamental absences

combined with a simple SDM, tested within its training range, highlights issues that are likely to

plague most correlative modelling efforts. These sources of model error can be broadly categorized

into model algorithm, scale, input data and covariates.

The most obvious cause for the observed over-prediction is BIOCLIM itself. As described previously,

the use of a rectilinear envelope and a simple algorithm (distance to the 50th percentile in climate

space), results in a coarsely-defined niche. The model will include neighbouring areas of climate space

in the envelope not represented by the species’ distribution, as long as they are between the minima

and maxima of climate variables. Additionally, the algorithm does not allow variable interactions. This

emphasizes the need to carefully select an SDM according to the question at hand, and be aware of the

limitations of each method (Kriticos et al. 2013). However, over-prediction was unexpectedly

observed within the training range of the model and at the species’ range limits (i.e. not in “corners” of

the rectilinear envelope unrepresented by the species’ distribution), so there must be additional sources

of error aside from the BIOCLIM model.

A potential second source of error is differences in scale (grain size) between BIOCLIM and IPM

projections, and that is not unique to this study. The SDM was fitted at 30 arc-seconds (WGS 1984,

approximately 1 km2) while the IPM predicts population growth at just one point within the grid cell.

Microhabitat conditions at the IPM point location might give inflated or deflated impressions of

suitability relative to average conditions in the grid cell. It could therefore be argued that this study

was not a fair test of BIOCLIM, but the problem of scale also applies to conventional tests of SDM

performance, which use point occurrence data for verification (Sinclair et al. 2010). A possible

solution could be to divide each grid cell into sub-samples and take the mean of all occurrences or, in

this case, λ values across each cell, thus comparing average climate to average suitability, but this

would require a quantity of data rarely available to modellers.

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Tangential to the issue of scale is that of input data. Most SDMs are calibrated on large data sets of

occurrence records collated from online databases (e.g. GBIF, http://www.gbif.org/), and there is a

wealth of literature detailing the ensuing biases and effect on model performance (Loiselle et al. 2007;

Wolmarans et al. 2010; Syfert et al. 2013). Consequences of sampling bias should be less severe for

simple profiling techniques such as BIOCLIM, because as long as the outer envelope is accurate, the

species’ distribution within it will only bias the relative scores of suitable grid cells, not whether sites

are classified as suitable or unsuitable. In addition to sampling bias, taxonomic uncertainties,

misidentification, and geo-referencing error could cause over-prediction. Although every effort was

taken to clean the data prior to model training (section 2.3.2), the study species are difficult to identify.

All Aeonium species hybridize readily and have high phenotypic plasticity (Lems 1960). Cotyledon

orbiculata has a disputed taxonomy, where some consider that regional varietals should be classed

unique species due to different habitat requirements (Van Jaarsveld & Koutnik 2004). Furthermore,

most SDMs weight all occurrences equally, so single outlier points (e.g. plants under indoor

cultivation or irrigation) can disproportionately influence projections (Kriticos et al. 2014). While I

removed cultivated plants from the BIOCLIM training data, it is possible that some occurrences

persisted in sink populations, or in microclimates within otherwise unsuitable grid cells. If so,

BIOCLIM would over-predict range limits (Warren 2012), as the SDM was tested against whether

grid cells could support self-sustaining, rather than sink, populations. These issues could be mitigated

by weighting input data by abundance, and while some studies have incorporated abundance data into

SDMs (de Villiers et al. 2013) that option is yet to be adopted widely.

A final source of uncertainty arises from climatic variables used in the SDMs. It is known that climatic

predictors should be chosen to reduce autocorrelation and according to the requirements of the species

(Elith 2013). I parameterised BIOCLIM using only five climatic variables, to minimize over-fitting.

While additional variables might have reduced some over-prediction, the risk of underestimating range

limits due to spurious correlations was deemed too high. A less obvious pitfall of climatic variables is

whether they accurately reflect real climatic conditions in an area. Most SDM efforts base projected

distributions on global interpolated data such as the freely-available Worldclim variables [(Hijmans et

al. 2005), available at http://www.worldclim.org/]. The Worldclim dataset projects temperature and

rainfall variables at up to 30 arc-second resolution interpolated from weather station point data, and is

averaged over a 30 or 50 - year period depending on the location. Where coverage is low, the accuracy

of the interpolated values is questionable (Soria-Auza et al. 2010) and areas such as Banks Peninsula

with high climate variation over small areas (as a result of topography) may be poorly approximated

by gridded climate data (Kriticos & Leriche 2010). In this study, BIOCLIM projections trained on

long-term, average climate data (Worldclim) were tested against IPM predictions derived from 2-year

averages at point locations. The IPM is immediately advantaged by using recorded data rather than

interpolations, and more biologically meaningful variables (e.g. growing degree days, frost days). For

example, no SDM of A. arboreum based on Worldclim data would differentiate the unsuitable

Canterbury Plains from the suitable coastline of Banks Peninsula, because a key limiting variable

http://www.gbif.org/


115

(frost days) is poorly represented by Worldclim’s “Annual minimum temperature”. For comparison,

recorded annual frost days were 63 at Christchurch Airport and 0 at Hays Bay (equivalent elevations,

but the former is unsuitable and the latter highly suitable), yet Worldclim estimates their mean

minimum temperatures to be 1.7 °C and 1.3 °C respectively. Whether testing the SDM against a model

driven by more accurate climate data is fair, depends on the question being asked. If that question is to

evaluate how intrinsically good BIOCLIM is as a model, it would need to be compared with an IPM

driven by the same Worldclim variables. But, this study was concerned with how BIOCLIM

projections compare with reality, so the IPM should mirror field observations as closely as possible.

It was beyond the scope of this study to determine the relative impact of the potential sources of over-

prediction, but the results demonstrate that validation against fundamental absences can give some

insight into model reliability. While some over-prediction stems from the BIOCLIM algorithm, there

are likely to be other sources of error common to all SDM studies, and comparing fundamental

absence data against a selection of SDMs could disentangle the relative importance of scale,

covariates, algorithm and training data. Regardless of the cause of the observed over-prediction,

BIOCLIM nonetheless appeared to rank sites adequately by suitability. To refine projections, I

demonstrated a simple method to remove a proportion of model over-prediction by altering the

threshold for suitability, which is a novel approach to combining process-driven models with SDMs.

By raising the threshold to better discriminate fundamental absences from both fundamental and true

presences, I was able to reduce the predicted suitable area by between 7% and 37%, depending on the

species, with minimal risk of under-predicting species’ ranges. While this is an improvement on the

original models, differences in specificity were minor because only range margins were adjusted and

over-prediction within the core climate envelope remained. However, for C. orbiculata in particular,

the refined projections may be useful for prioritizing areas for control. The implications for the future

spread of the three species on Banks Peninsula are discussed in Chapter 6, within the context of the

findings of previous chapters.

5.5.3 Limitations

Though the refined maps are an improvement on the original BIOCLIM projections, they are still a

liberal estimate of range limits because only the outer extremes of the climate envelope were trimmed.

Substantial over-prediction of suitable climate (e.g. the Canterbury Plains) remains. Furthermore, the

IPM does not predict actual population growth rates, principally because at many locations there are

currently no populations to model and seed rain is unknown. Lambda was modelled in the steady state

over a 2-year period, using a closed system (i.e. no immigration or emigration) and the IPM assumed

that all viable seeds had an opportunity to germinate. The IPMs used in this chapter were fully

deterministic, and therefore may over-predict suitable conditions at range margins where populations

may be vulnerable to environmental stochasticity (Parmesan et al. 2000; Hargreaves et al. 2014).

While there is room for improvement in the IPMs, they provide a close approximation to actual

climatic suitability for the study species, as they essentially combine multiple observations from high

116

powered field surveys into a single measure of suitability. As demonstrated, the IPMs provide a better

measure of model performance than occurrence data alone, and allow more confident assertion of the

species’ climatic limits.

It is important to emphasize that the final projections represent climatic suitability only. Especially for

succulent geophytes, many other environmental factors will determine whether a site is invaded

including soils, rock type and land use. Very little is known about the dispersal capabilities of these

species other than they produce microscopic (~ 500 µm length) wind-dispersed seeds. I have therefore

assumed no barriers to dispersal. However, wind patterns may play a part in the direction and speed of

invasion for these species. The question of non-climatic suitability could be addressed by applying the

land use and habitat masks developed in Chapter 2, but at the scale of Banks Peninsula it would be

beneficial to have prior knowledge of whether certain rock or soil types are suitable. Finally, the

thresholding technique used here is somewhat experimental, and removes only those areas that are at

the outer edges of the climatic envelope. Estimates could be improved substantially by using finer

scale and more appropriate climate data informed by the field experiments, and using the IPM results

as presence/absence data to feed an invaded range SDM for Banks Peninsula [a similar methodology

to Elith et al. (2010)]. The methodology presented here is discussed further in Chapter 6, along with

potential future work.

5.5.4 Conclusions

This study has demonstrated a novel method of integrating plant performance data with SDMs. Field

data describing vital rates were used to parameterize a climate-driven IPM and predict population

growth (λ) at 83 locations in the study region. The population parameters (λ) were then converted to

fundamental presence/absence data, reflecting whether climatic conditions are conducive to self-

sustaining populations. Fundamental presences/absences were used to validate and refine existing

BIOCLIM projections, and this method could be applied to other SDMs to improve confidence in

projections. I demonstrated that BIOCLIM was a better predictor of plant performance than would be

indicated by conventional cross-validation techniques (using occurrence data) alone. However, I found

that BIOCLIM over-estimated suitable climate not just within the core “envelope” but also,

unexpectedly at range limits. Likely causes of over-prediction include coarse representation of the

niche by BIOCLIM, differences in grain size of validation tools versus projections, and quality of

climate and occurrence data in training the SDM. The latter three issues are likely to affect most

correlative SDM efforts. The BIOCLIM projections were nonetheless useful as they ranked sites well,

and I refined projections by iteratively raising the threshold to best fit IPM predictions. Thus, the over-

prediction at range edges was minimized and projections of the species’ potential distributions were

improved. Where possible, I encourage the use of fundamental presence/absence data in addition to

presence data, and in place of pseudo- or true absence data, for testing and improving SDMs of non-

equilibrium species.

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Chapter 6 - General discussion

6.1 Summary of findings

The aims of this thesis were to test the ability of correlative SDMs to predict real-world plant

performance, and to integrate data from SDMs with survey and experimental data on actual plant

performance to improve model projections. I applied this approach to three non-native succulent

species naturalized in New Zealand; Aeonium arboreum, A. haworthii and Cotyledon orbiculata. My

key questions were:

1. Are the current distributions of A. arboreum, A. haworthii and C. orbiculata in New Zealand

climatically distinct from their distributions elsewhere, and what are their potential

distributions as estimated using SDMs?

2. Is there evidence that climate limits the distributions of these species on Banks Peninsula, and

how do demographic processes correlate with climate within and beyond the species’ current

distributions?

3. Is variation in fecundity in naturalized populations on Banks Peninsula related to variation in

local climate?

4. How well do SDMs predict the actual performance of the target species on Banks Peninsula,

and can field data be used to improve SDM projections?

I used simple correlative SDMs to project suitable climate for the three species globally, and in New

Zealand (Chapter 2). The importance of non-climatic effects on the species’ distributions was inferred

via a combination of a priori reasoning and spatial analysis, and consequently climate-only models

were refined by topography and land use. Results also indicated that the species’ current distributions

in New Zealand constituted a shift in their realized climatic niches. For the remainder of the thesis I

focussed on climatic drivers within Banks Peninsula, Canterbury. A field transplant experiment

(Chapter 3) provided evidence of strong climatic limitation to survival, germination and growth in all

three species with increasing elevation. The responses of Aeonium species were similar and

germination, growth and survival declined sharply above 300 - 400 MASL. Meanwhile, C. orbiculata

was inconsistently limited by elevation and climatic covariates, and was mortality was predicted to be

relatively low (< 75%) up to 300 m above current limits (681 MASL). Because growth and mortality

were intrinsically linked, it was difficult to infer likely elevation limits for C. orbiculata. In contrast,

surveys of naturalized populations (Chapter 4) uncovered scant evidence of climatic limitation to

fecundity across the species’ current distributions. Plant size was the most consistent predictor of

fecundity, and it was unclear whether this was an indirect effect of climate. I integrated field data by

incorporating the linear regressions of mortality, growth and fecundity against climate into an integral

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projection model (IPM). Predicted lambda values from the IPM were converted into fundamental

presence/absence data (i.e. whether self-sustaining populations were predicted), and used to validate

the previous climate-only SDMs. The SDMs over-estimated climatic suitability, and so the suitability

threshold was lowered to be as parsimonious as possible with predicted lambda. This reduced over-

prediction of outer climatic limits in the region, and provided more realistic projections for Banks

Peninsula. However, a significant amount of over-prediction remained within the suitable “envelope”.

Potential causes of the over-prediction were discussed, most of which are likely to be relevant to all

correlative SDM attempts. Because my final data chapter achieved many of the aims of a thesis

“synthesis” chapter by drawing together the previous findings, I instead focus my discussion on the

study species on Banks Peninsula, only briefly discussing the broader aspects of the modelling work.

6.2 Species distribution models vs. reality

6.2.1 How well did SDMs predict plant performance?

I was limited in my choice of SDM by the study species’ traits and the characteristics of the

distribution data. Because of the disjunct distributions of the three species, I chose one of the oldest

SDM algorithms, BIOCLIM (Nix 1986), a simple envelope or “boxcar” technique. This method

avoided under-predicting suitable habitat at the expense of a high likelihood of over-prediction.

Although cross-validation techniques used in Chapter 2 indicated that the SDM performed well, the

IPM revealed substantial model over-prediction on Banks Peninsula. However, BIOCLIM was able to

rank sites well enough in accordance with lambda to achieve a satisfactory AUC (> 0.7). It therefore

provided a useful, but over-generous estimation of suitable climate and I demonstrated a simple

method of eliminating as much of this over-projection as possible.

The relatively poor performance of BIOCLIM raises the question of whether it was, in fact, the best

method for modelling the three species. I considered BIOCLIM the best option for a global model of

the three species’ distributions, as the disjunct distributions would cause more complex models

e.g. MaxEnt (Phillips et al. 2006), to under-predict potential ranges. Since then, another presence-only

method, range-bagging (Drake 2015) has been developed, which might have been superior. Training

the SDMs and niche analyses on global data demonstrated that the species’ New Zealand distributions

are climatically distinct from their distributions elsewhere, and that the extent of their naturalization in

New Zealand could not have been predicted prior to their introduction. However, the native ranges for

all three species told us little about their potential distributions in New Zealand, and in the case of

C. orbiculata, led to over-prediction of suitable climate because of the inclusion of frost-tolerant high

elevation populations. In retrospect, a model trained on New Zealand data only [an invasive species

distribution model, or iSDM; (Václavík & Meentemeyer 2009)] could have been informative as a

follow-up to the global model. Removing the native ranges from training data would not sacrifice

useful information, as the climatic conditions are so distinct, and would eliminate the problem of

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disjunct distributions. An iSDM would allow the use of more complex algorithms that are less likely

to over-estimate potential distributions (e.g. boosted regression trees, MaxEnt).

As discussed in Chapter 5, it was not possible to determine how much over-prediction stemmed from

BIOCLIM itself, versus other sources of error common to all SDM studies. To recap, other potential

sources of error are quality of occurrence data, accuracy of climate layers, and scale. Occurrence data

may bias models where there are errors in species identification or confusion over taxonomy (Elith et

al. 2013), sampling bias [though methods exist for minimizing bias e.g. Dorazio (2014)], or where

species are persisting in otherwise unsuitable locations [for example plants in cultivation, or sink

populations (Warren 2012)]. Climate layers do not always reflect true site conditions, as they are

interpolated from weather station data and are often inaccurate where stations are rare (Niekerk &

Joubert 2011). Scale introduces error when occurrence locations, which are usually point data, are not

representative of the average conditions in the grid cell. Examples of this are populations persisting in

microclimates, or where there is high climatic variation within the grid cell [e.g. Kriticos et al.

(2014)]. Without further investigation, this discussion remains speculative, as it is not possible to

attribute the proportion of error to each source. I encourage the consideration of the aforementioned

sources of error in all modelling efforts, whether using complex or simple algorithms.

6.2.2 Improving SDM accuracy

This thesis has highlighted the importance of selecting an SDM algorithm based on species’ traits and

occurrence data, as well as performing prior niche analyses to identify disjunct or non-analog

distributions. I have demonstrated an effective method of testing SDM projections against plant

performance data, and argue for using fundamental absences in place of pseudo or true absences when

modelling non-equilibrium species, if possible. However, drawing general conclusions on the accuracy

of SDMs, and relative importance of sources of error, is difficult from this case study alone. More

generality could be achieved by repeating the methods described in Chapter 5 for a selection of

species, varying the quality of occurrence data, climate layers, grain size and SDM algorithm to

identify the relative impact of each source of error on SDM performance. Although other studies have

compared performance of different models and other error sources (Aguirre-Gutiérrez et al. 2013;

Syfert et al. 2013; Qiao et al. 2015; Stoklosa et al. 2015), none have used fundamental absences, thus

it is difficult to determine to what extent reportedly good models are simply overfitting the data.

Using fundamental presences and absences to validate SDMs is appealing, but may be difficult to

implement widely. To parameterize the population model, predicted vital rates are required as a

function of climate (or other variables included in the SDM being tested, such as soil), and this is data-

intensive. The cost of gathering the necessary data may be prohibitive, and is at odds with the primary

appeal of SDMs, namely, that they are fast and cheap. If a species is well studied, however, it could be

possible to gather sufficient information from existing literature to parameterize a simple population

model. In this case, more thorough validation of the population model would be required if it was

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parameterized using data from other regions, but it could be a viable alternative to extensive field

trials. Alternatively, other studies have used performance data for one or two vital rates alone to

validate models, rather than predicting population growth (Pattison & Mack 2008; Sheppard et al.

2014). Although more cost-effective than developing full population models, performance data is

reliable only if the limiting vital rate is known (e.g. germination), and it is difficult to determine where

vital rates become limiting without an intuitive suitable/unsuitable binary classification, such as that

provided by lambda. Furthermore, a priori assumptions of limiting processes may not always be

correct. For example, based on existing literature I incorrectly expected annual internodes to be a good

indicator of performance in Aeonium species.

In lieu of field experiments, surveys of wild populations could provide the necessary data if accidental

release of the organism is too risky (e.g. the species is a restricted organism), but only under certain

conditions. This is not valid for species that are far from equilibrium, such as the early stages of

invasions (Thuiller et al. 2006; Wilson et al. 2007), and sampling marginal populations is desirable for

robust extrapolation (Hargreaves et al. 2014). Identifying marginal populations prior to sampling is,

admittedly, difficult. As a final alternative, laboratory-based studies are cheaper and more efficient

than field studies, and could provide the necessary parameters for a climate-driven IPM or similar.

This would be most practical for fast-growing annual species. But, responses observed in the

laboratory may translate poorly to the field. In this scenario, it might be more useful to collect

physiological data to parameterise a mechanistic model, though mechanistic models are not always

superior to their simpler correlative counterparts due to compounding of error (Buckley et al. 2010).

6.3 The future of non-native Crassulaceae on Banks Peninsula

6.3.1 Climatic limitation

The second of the two central themes of this thesis was to define the climatic limits of A. arboreum,

A. haworthii and C. orbiculata on Banks Peninsula. The field experiment established clear evidence of

climatic limitation in the region. Regional spread cannot continue indefinitely, as all three species

were limited to varying degrees by the elevation and precipitation gradient. High precipitation limited

seedling establishment in C. orbiculata (and A. arboreum to a lesser extent), and is likely to mitigate

spread of these species the wetter southeast parts of the region. High elevations were limiting to

growth and survival for all three species, and for Aeonium species to seedling establishment also. The

results of combining the field data into IPMs were consistent with previous findings in this thesis.

Overall, Aeonium species had clear climatic limits and the IPMs predicted negative population growth

at most high-elevation or high-frost sites. Of the sites that the IPMs predicted to be suitable for

A. arboreum, 38% are currently unoccupied, versus 31% for A. haworthii, indicating that further

spread of both species is likely. Once the IPMs were used to refine the BIOCLIM projections, both

Aeonium species had similar predicted range limits, and most high elevation or inland areas of Banks

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Peninsula were excluded as potential invasion sites. The similarity of the two Aeonium species’

potential distributions might appear surprising due to their different origins (Canary Islands vs.

Morocco), but the Aeonium genus, while diverse, has low genetic diversity (Mes & T'Hart 1996). As a

result, much of the genus’ morphological variety may be due to phenotypic plasticity and flexible

niche occupation (Jorgensen 2002). According to the refined projections of suitable climate, the main

difference between the two species is that A. haworthii could persist at slightly higher elevations than

A. arboreum, accounting for the difference in projected suitable area (51% of Banks Peninsula for

A. arboreum, versus 70% for A. haworthii). This is consistent with their niches in the native range,

where A. arboreum is found at lower elevations and is thought to be less adaptable to climatic

extremes (Lems 1960). The final adjusted BIOCLIM projections indicated that, of the 871 30 arc-

second grid cells surveyed (Figure C.1), only 5% of those predicted to be suitable currently contain

A. arboreum, and 6% for A. haworthii.

The IPMs and BIOCLIM both predicted suitable climate at higher elevations for Cotyledon orbiculata

than the Aeonium species, but climatic limits of this species were less clear-cut. Only 16 out of 83 IPM

sites were predicted to be unsuitable, in contrast with 41 for both Aeonium species. Unsuitable sites for

C. orbiculata were mainly those with highest elevation and precipitation. Out of the sites predicted to

be suitable, 48% are currently unoccupied, indicating a greater potential for spread than either

Aeonium species. Because the original BIOCLIM model classified the entire Peninsula as climatically

suitable, the refined projections were less certain for C. orbiculata, but they eliminated the wettest and

highest elevation sites in the region. The thresholding for C. orbiculata removed a much greater

proportion of suitable grid cells for either Aeonium species, resulting in a similar projection to

A. haworthii. Thus, the BIOCLIM projections for C. orbiculata were over-predicting to the greatest

degree. The final projections indicated that approximately 63% of Banks Peninsula is likely to be

climatically suitable, and of the grid cells surveyed, only 19% of those predicted to be suitable

currently contain C. orbiculata.

6.3.2 Non-climatic limitation, implications for spread

Climatic limits are just one piece of the invasion puzzle, and the fact that A. haworthii has the greatest

proportion of climatically suitable area does not necessarily mean it poses the greatest risk. Non-

climatic effects will shape the distribution of each species, and these are discussed in Chapter 2.5 in

relation to their global and New Zealand distributions, and Chapter 3.5 in relation to the elevation

gradient on Banks Peninsula. Currently, much of how the species respond to non-climatic factors is

unknown, but it is possible to draw the following conclusions. Aeonium species are likely to be

restricted to similar habitats to each other and to where they currently occur. I expect spread within

climatically suitable areas to be limited to cliffs, roadsides, and other bare or sparsely vegetated

surfaces. Because the genus has no grazing defences it should remain absent in pasture (Jorgensen &

Olesen 2001), and because of the low photosynthetic capacity of CAM, where interspecific

competition is high (Luttge 2004). Climate will define the broad limits of the two species on the

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Peninsula, preventing establishment inland or at high elevations, which is encouraging as the high

elevation rock outcrops are refugia for a number of local and national endemic species (Wiser &

Buxton 2009). Spread appears likely to continue around the coastline of the Peninsula, the volcanic

cliffs of which are recognized as naturally uncommon ecosystems (Holdaway et al. 2012). The spread

of Aeonium species should be slow in comparison to C. orbiculata as habitat is more limiting, thus

lowering the probability of seed landing in suitable environments. Assuming only climate and habitat

are limiting to both Aeonium species, and that other non-climatic effects are not relevant

(e.g. substrate, anthropogenic effects), they should eventually form a patchy distribution around the

coastline and up to around 400 MASL once they reach equilibrium.

On Banks Peninsula, C. orbiculata appears to be more limited by climate than by other factors. I

expect spread to continue along the coastline and inland up to approximately 400 MASL in the

northern bays, but as C. orbiculata is also limited by precipitation it is unlikely to spread far from the

coast in the Southeast. It is found on a wide variety of substrates (Van Jaarsveld & Koutnik 2004), and

in habitats that are common in the region (i.e. pasture, cliffs, outcrops and roadsides). Cotyledon

orbiculata is likely to be absent under canopy because of the correlation between solar radiation and

fecundity (Chapter 4) and the negative effect of canopy cover on growth (Chapter 3). Some small

populations of C. orbiculata occur under pine on the Peninsula (e.g. survey site Pigeon Bay 2), but the

plants have a distinct growth form with minimal branching and large leaves lacking epicuticular wax,

consistent with the findings of Barker et al. (1997). I observed no flowering in these populations. I

expect C. orbiculata to remain absent from the approximate 12% of the region covered by native

forest, as it has a denser canopy than pine. As with Aeonium species, there are additional factors

(e.g. soil type) that could be limiting to C. orbiculata. Based on the evidence collected in this thesis

however, I expect C. orbiculata to eventually reach a less patchy, more widespread distribution than

Aeonium species. Spread of C. orbiculata is likely to be more rapid as the probability of dispersing to

suitable areas is higher, and vegetative spread by trampling in pasture may accelerate the process.

I therefore encourage the control of C. orbiculata on Banks Peninsula, both for economic and

ecological reasons. The species poses a threat to the region’s cliffs and outcrops, and associated rare

species, but also could cause stock losses in the event of poisonings. All three species are probably too

well established in the region to make eradication feasible, but further spread around the eastern bays

could be contained. The southwestern bays are a particular cause for concern, as while the three

species are currently absent, models indicate high climatic suitability and nearby populations of

Birdling’s Flat could provide a substantial seed source, especially for C. orbiculata. If possible, the

three species should be removed from Birdling’s Flat entirely. Raising awareness of C. orbiculata’s

toxicity to livestock might encourage voluntary removal of the species by landowners.

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6.4 Avenues for future research

6.4.1 Study species – some important unknowns

The climatic limits of A. arboreum, A. haworthii and C. orbiculata on Banks Peninsula have been

established, but some unanswered questions remain that are relevant to their potential distributions.

Quantifying seed bank longevity, seed dispersal, individual life span, and fecundity beyond current

range limits for the three species would allow for temporally explicit projections of spread. More

interestingly, the strength of biotic interactions and their effects on population dynamics remain

unknown. While insect pollination occurs in all three species, Aeonium species are also pollinated

abiotically, and all are also capable of autogamy (Alamo et al. 1996; Zietsman 1998). There are

anecdotal tales of C. orbiculata being pollinated by New Zealand birds (Di Carter, pers. comm. 2010),

which is plausible given that sunbirds are pollinators in its native range. If autogamy lowers seed

output and progeny fitness in Aeonium species as it does in C. orbiculata (Zietsman 1998), pollinator

interactions could strongly influence rates of spread for all three species.

Similarly, natural enemies and the effect of competition on the three species are unknown, though I

hypothesized that interspecific competition is an important factor in habitat selection, given the low

photosynthetic capacity of CAM plants. In the Canary Islands, Aeonium species are found only in

specific habitats and regions, and Lems (1960) posits interspecific competition and adaptive radiation

as underlying mechanisms. As a consequence of interspecific competition, I expect land use to be an

important factor for all three species, and hypothesize that grazing facilitates C. orbiculata invasion by

reducing competition and increasing vegetative spread. This hypothesis could be explicitly tested by

grazing exclusion field trials [e.g. similar to studies of other succulents by Moolman and Cowling

(1994) and Dean et al. (2015)] and would establish whether C. orbiculata can persist amongst

vegetation without herbivores.

All three species have unanswered questions related to their taxonomy that merit further investigation.

One of these is the effect of hybridization in Aeonium species, which hybridize readily (Jorgensen &

Olesen 2001). Supposedly, natural hybrids are rare in the native ranges (Lems 1960) but on Banks

Peninsula, they are common to the point that identification to species level can be difficult (Bill Sykes,

pers. comm., 2010). Natural hybrids might affect the genetic diversity of Aeonium populations and

their climatic tolerances, thereby shaping range limits, as such studying the genetics of natural

populations and testing climatic limitation in hybrids could be beneficial. Meanwhile, the taxonomy of

C. orbiculata is highly contested (Van Jaarsveld & Koutnik 2004), with debates over classifying the

five varietals as distinct species that are unlikely to be resolved soon (Ernst Van Jaarsveld, pers.

comm., 2014). In this thesis, I offered a hypothesis that the less-hardy regional populations of South

African C. orbiculata such as those in coastal areas (Van Coller & Stock 1994) may be ancestral to

those in New Zealand. Genetic or historical studies in New Zealand and South Africa could pinpoint

the South African origins of New Zealand introductions. Such studies could improve projections of the

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species’ potential distributions by establishing whether the extremely frost-tolerant genotypes of

C. orbiculata are present in New Zealand. Finally, and perhaps most interestingly, the apparent

climatic niche shift in all three species in New Zealand relative to their global ranges merits further

investigation. While New Zealand is undoubtedly novel climate for all three species, it is not feasible

to distinguish realized from fundamental niche shifts from correlative approaches alone (Guisan et al.

2014). There are numerous reports of niche shifts during invasions (Broennimann et al. 2007; Mata et

al. 2009; Gallagher et al. 2010), but the underlying mechanisms have rarely been investigated

empirically (Petitpierre et al. 2012). Alien Crassulaceae in New Zealand could provide an ideal case

study due to the dramatic climatic differences between ranges. Fully reciprocal transplant experiments

between New Zealand and the native ranges would evidence whether the phenomenon can be

considered a fundamental niche shift or not, while phylogenetic analyses could investigate underlying

mechanisms, e.g. whether the shifts arise from evolutionary changes or are in fact a result of

underlying phenotypic plasticity or exaptation. These species present an opportunity to improve our

understanding of niche shifts and their mechanisms.

6.4.2 Limitations, and lessons learned

The majority of limitations have been discussed in corresponding chapters, but it is important to

emphasize that the final refined projections for Banks Peninsula still over-predict suitable climate

(over-prediction rate was 27%, 24% and 5% for A. arboreum, A. haworthii and C. orbiculata,

respectively). Final projections also do not account for habitat suitability, thus they are valuable

starting points but not predictions of spread. As discussed earlier, fine-scale iSDMs trained on the

fundamental presence and absence points could improve projections for Banks Peninsula significantly.

In addition, there is room for improvement in the IPMs. Some parameters were omitted (e.g. seed

bank), population growth was predicted only in the steady state, and fecundity parameters were

extrapolated from surveys. The IPMs could also be improved by running multiple simulations to

estimate stable values of lambda that allow colonization. However, this would require temporally

explicit projections that incorporate stochasticity, and an estimate of seed rain to un-colonized sites.

Some of the limitations of this thesis have highlighted issues to bear in mind in future work, the most

important being choice of study species. While A. arboreum, A. haworthii and C. orbiculata are

biologically interesting and of immediate concern to local practitioners, they are far from ideal species

for a modelling exercise. In hindsight, other characteristics would have been desirable, for example,

the species should not have highly restricted microhabitat requirements that are unlikely to be

represented at a 1 km grid resolution, and should ideally not have a disjunct distribution in climate

space or non-analog climate between the native and invaded ranges. A well-studied species would

ensure a higher quality of distribution data in the native range, as well as sound a priori reasoning for

choosing climatic variables and understanding the role of non-climatic effects. An annual or fast-

growing species would maximise changes in demography or vital rates over a two-year field season.

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Despite all of this, it was exciting to work with species that have scarcely been studied, and I am

grateful for the opportunity to contribute to our understanding of the Crassulaceae.

6.5 Conclusions

To summarize, my four thesis objectives were answered as follows;

1. The current distributions of A. arboreum, A. haworthii and C. orbiculata in New Zealand are

climatically distinct from their distributions elsewhere, and this constitutes a shift in at least

the realized niches into cooler and wetter climatic conditions. I provided SDM projections of

the species’ potential distributions at a national scale, although it was necessary to use simple

models.

2. Performance was strongly climate-limited along the gradient present on Banks Peninsula, and

declined with increasing elevation and precipitation. Beyond the species’ current distributions,

at higher elevations, performance declined. The decline in performance was sharpest for

Aeonium species, but none of the three species have yet reached climatic equilibrium.

3. Fecundity varied significantly within and among wild populations on Banks Peninsula, but

very little of this variation was directly linked to climate. Plant size was the key predictor of

fecundity, and across their current distributions in the region, climate does not appear to limit

reproduction.

4. Testing SDMs against predicted population growth revealed that the SDMs over-predicted

suitable climate, both at range edges and within the “climate envelope”. It appeared unlikely

that the over-prediction was solely because of the SDM algorithm. Scale, occurrence data and

climate data are also likely sources of error, factors that are relevant to all SDM studies.

Despite over-prediction, SDM and higher predicted population growth were ranked similarly,

so projections were refined to improve estimates of range limits on Banks Peninsula.

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Appendix A – Supporting information for Chapter 2

A.1 An example MaxEnt model

To illustrate the problem of creating response curves to frequency distributions that are clustered and

disjunct in climate space, I ran a model in MaxEnt v.3.3.3k (Phillips et al. 2006) for a hypothetical

species. I created a samples with data (SWD) file for a species “Y”, with 300 occurrences at arbitrary

latitude and longitudes (WGS 1984). In the SWD file was only one variable of interest, “X”, which

was assigned values at each occurrence location to produce the disjunct frequency distribution shown

in Figure A1. In the same SWD file, I created 10 000 background occurrences, again with arbitrary

latitude and longitudes, with values of X equally distributed across the range. I ran two models trained

on this data. The first was run using linear and quadratic features only, to create smooth, “biologically

reasonable” response curves that would be a robust choice when extrapolating. The second model was

run using all “auto-features”, the commonly-used default settings. I used only one replicate per run,

and did not project the models. Response curves to variable X were exported and plotted against

frequency distributions in R (R Core Team 2014). Using either smoothed curves (a), or complex

responses (b), MaxEnt will under-predict the range of suitable climates for species Y. I emphasize that

this is not confined to MaxEnt; other SDMs may produce similar responses (Webber et al. 2011).

Figure A.1 Distribution of species Y in relation to a climatic variable X. Response curves (red)

generated by a MaxEnt model with linear and quadratic features only (a), and all “auto-features” (b).

In region 1 (R1), the species is most prevalent and occupies a wide range of climates, but can tolerate

conditions in region 2 (R2) although it is less prevalent. Values of X between R1 and R2 are assumed

to be climatically suitable. In a), suitable habitat in R2 is under-predicted, while in b), climate space

between R1 and R2 is under-predicted.

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A.2 Supporting data for study species

Table A.1 Sources and number of occurrence records collected for Aeonium arboreum, A. haworthii and Cotyledon orbiculata, before data cleaning and resampling.

Type Source A. arboreum A. haworthii C. orbiculata Available at:

Data Portals

GBIF 209 105 555 http://data.gbif.org

NZVH 26 46 18 http://www.virtualherbarium.org

NZBRN 1 1 4 http://www.nzbrn.org.nz

SANBI 305 http://sibis.sanbi.org

BIOTA (Jürgens et al. 2011) 7 http://www.biota-africa.org

Herbaria (Digitised

and non-digitised

specimens)

CHR 16 15 19 http://www.landcareresearch.co.nz/resources/collections/allan-herbarium

WAIK 1 http://www.nzherbaria.org.nz/herb_details.asp?NZHerb_ID=16

WELTU 1 http://www.victoria.ac.nz/sbs/research/facilities/herbarium

Articles

Healy (1959) 3 http://rsnz.natlib.govt.nz/

Mason (1978) 1 http://bts.nzpcn.org.nz/

Molloy (1980) 1 http://bts.nzpcn.org.nz/

Sykes (1992) 3 http://bts.nzpcn.org.nz/

Cameron (1996) 3 http://bts.nzpcn.org.nz/

Burrows (2001) 1 https://sites.google.com/site/nznaturalsciences/home/archived-issues

Surveys

Wilson (1983) 7 https://nvs.landcareresearch.co.nz/Data/DatasetDetails/2424/13248

Carter (2006) 32 79 https://nvs.landcareresearch.co.nz/Data/DatasetDetails/2370/10859

Ministerio de Agricultura Alimentación y

Medio Ambiente (2005)

50 http://www.magrama.gob.es/es/biodiversidad/servicios/banco-datos-

naturaleza/informacion-

disponible/atlas_manual_habitats_espanioles.aspx Carter (2014) 1 65

Pannell (2010) 41 36 186

Personal

communication

Broker, Gary (2010) 2

Carter, Di (2011) 13

Jackson, Jill (2010) 1

Hulme, Philip (2012) 2

Rentoul, Sandy (2010) 1

Smith, Kathryn (2010) 1

Smith, Paula (2010) 2

Waghorn, Robin (2010) 7

Ater, Mohammed (2011) 7

Fennane, Mohammed (2011) 2

Other Google Street View 6 10 3 http://maps.google.com

Bramwell & Bramwell (1990) NA

http://data.gbif.org/

http://www.virtualherbarium.org/

http://www.nzbrn.org.nz/

http://sibis.sanbi.org/

http://www.biota-africa.org/

http://www.magrama.gob.es/es/biodiversidad/servicios/banco-datos-naturaleza/informacion-disponible/atlas_manual_habitats_espanioles.aspx



http://maps.google.com/

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Table A.2 Regions and Köppen-Geiger (KG) classes sampled within for Aeonium arboreum,

A. haworthii and Cotyledon orbiculata niche analyses, and number of samples taken.

Species Sampling areas Background

samples

Main climate

KG classes

Precipitation/temperature

KG sub-classes

A. arboreum Australia

Balearic Islands

Canary Islands

Madeira

Malta

Morocco

New Zealand

Portugal

Spain

U.S.A.

22 609 Arid Desert, hot

Steppe, cold

Steppe, hot

Warm temperate

Fully humid, warm summer

Summer dry, hot summer

Summer dry, warm summer

A. haworthii Australia

Canary Islands

France

New Zealand

Spain

U.S.A.

13 676 Arid Steppe, cold

Warm temperate




C. orbiculata Angola

Australia

Corsica

Lesotho

Namibia

New Zealand

Mozambique

South Africa

Spain

Swaziland

U.S.A.

35 924 Arid Desert, cold

Desert, hot

Steppe, cold

Steppe, hot

Warm temperate

Fully humid, hot summer




Winter dry, hot summer

Winter dry, warm summer

129

a) i) a) ii) a) iii)

b) i) b) ii) b) iii)

c) i) c) ii) c) iii)

d) i) d) ii) d) iii)

e) i) e) ii) e) iii)

Figure A.2 Frequency histograms of the five bioclimatic variables used in niche analysis and models

of target species, at all global occurrence points. Plots shown for i) Aeonium arboreum;

ii) A. haworthii and iii) Cotyledon orbiculata. Variables are: a) BIO10 (Mean temperature of the

warmest quarter, °C × 10); b) BIO11 (mean temperature of the coldest quarter, °C × 10); c) BIO16

(Precipitation of the wettest quarter, mm); d) BIO17 (Precipitation of the driest quarter, mm);

e) BIO19 (Precipitation of the coldest quarter, mm).

130

Figure A.3 Frequency of land use classification (Nachtergaele & Petri 2008) in grid cells (5 arc-

minutes) containing Cotyledon orbiculata in a) Southern Africa (South Africa, Lesotho, Swaziland,

Namibia, Mozambique, Angola); b) Europe (Corsica, Spain); c) the U.S.A.; d) Australia and e) New

Zealand. Asterisks denote significance of land use type given its proportional area, according to

Fisher’s exact test (• = p < 0.05, = p < 0.01).

131

Figure A.4 Density of cattle, goats and sheep (heads per km2) in grid cells (0.05 decimal degrees) containing Cotyledon orbiculata (grey) versus randomly-selected

background points (white) in a) U.S.A., b) Europe (Corsica, Spain), c) Southern Africa (South Africa, Lesotho, Swaziland, Namibia, Mozambique, Angola), d)

Australia and e) New Zealand. Maximum density shown where whiskers extend beyond axes. Data courtesy of GLW (Robinson et al. 2014).

132

Figure A.5 Livestock density of cattle, goats and sheep expressed as heads per km2 in grid cells (0.05 decimal degrees) containing Aeonium arboreum (grey) versus

randomly-selected background points (white) in a) U.S.A., b) Europe (Spain, Portugal, Balearic Islands, Malta), c) Macaronesia (Canary Islands, Morocco,

Madeira), d) Australia and e) New Zealand. Maximum values shown where whiskers extend beyond plots. Data courtesy of GLW (Robinson et al. 2014).

133

Figure A.6 Livestock density of cattle, goats and sheep expressed as heads per km2 in grid cells (0.05 decimal degrees) containing Aeonium haworthii (grey) versus

randomly-selected background points (white) in a) U.S.A., b) Europe (Spain, France), c) Macaronesia (Canary Islands), d) Australia and e) New Zealand. Maximum

values shown where whiskers extend beyond plots. Data courtesy of GLW (Robinson et al. 2014).

134

Figure A.7 a) Frequency of Cotyledon orbiculata occurrence records in land cover classes (Ministry

for the Environment & Landcare Research 2014) and b) farm types (excluding non-farmland)

according to Agribase™ (AsureQuality 2006). Black bars indicate statistical significance (p < 0.01) of

C. orbiculata frequency, given total occurrences and the proportional area of each class in New

Zealand, according to a one-tailed binomial test.

135

Table A.3 Description of land cover classes (Ministry for the Environment & Landcare Research

2014) that spatially intersect Cotyledon orbiculata occurrence records in New Zealand. Class

descriptions summarized from Thompson et al. (2003).

Class Name Description

UPO Urban Park/Open Open, mown, grassed amenity areas within or associated with

BU.

R River Natural and modified rivers, creeks, canals and channels over

30 m wide.

MK Manuka/Kanuka Indigenous shrubland, often lightly grazed. Early successional

scrub on previously forested land with history of burning.

MES Mixed Exotic Shrubland Single-species or mixed introduced exotic shrubs and climbers.

LPG Low Production

Grassland

Exotic or indigenous grassland, low vegetation vigour. Lower soil

fertility, low fertilizer application, seasonal drought or short

growing season. Usually managed for sheep and beef grazing,

steep slopes.

IF Indigenous Forest Indigenous tall forest canopy species, identified from ground

surveys.

HPEG High Production Exotic

Grassland

Intensively managed exotic grassland, with good vegetation

vigour. Usually rotationally grazed. Fertilizer and irrigation may

be used.

FH Forest Harvested Areas of forest showing evidence of harvesting since LCDB1.

EF Exotic Forest Exotic forest other than Pinus radiata, e.g. Douglas fir, Acacia or

Eucalyptus.

BU Built Up CBDs, suburbs, commercial/industrial, hard surfaces e.g. roads,

paved areas.

BIH Broadleaved Indigenous

Hardwood

Usually high rainfall areas, also low-growing coastal broadleaved

forest. Mixture of native broad leaved hardwood species.

136

Figure A.8 Global a) and New Zealand b) projections of BIOCLIM models for Cotyledon orbiculata, trained on subset of all occurrence data, with 7 points removed

from the most extreme high elevations in Lesotho. BIOCLIM scores are percentiles of the species’ distributions in climate space. Scores approaching 1 signify

similarity to the species’ 50th percentile in climate space (“core” climate), and 0 signifies that the cell is outside of the species’ rectilinear hypervolume.

137

Appendix B – Supporting information for Chapter 3

Figure B.1 Map of current distributions, cutting collection sites and seed collection sites, for

a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata on Banks Peninsula. Location of

Banks Peninsula relative to New Zealand also shown (d).

138

Table B.1 Source list for Banks Peninsula distribution data of Aeonium arboreum, A. haworthii and Cotyledon orbiculata.

Type Source A. arboreum A. haworthii C. orbiculata Available at:

Data Portals GBIF 25 32 9 http://data.gbif.org

NZVH 21 35 http://www.virtualherbarium.org

Herbaria* CHR 9 5 9 http://www.landcareresearch.co.nz/resources/collections/allan-herbarium

WAIK 1 http://www.nzherbaria.org.nz/herb_details.asp?NZHerb_ID=16

Articles Healy (1959) 1 http://rsnz.natlib.govt.nz/

Burrows (2001) 1 https://sites.google.com/site/nznaturalsciences/home/archived-issues

Surveys

Wilson (1983) 7 https://nvs.landcareresearch.co.nz/Data/DatasetDetails/2424/13248

Carter (2006) 32 79 https://nvs.landcareresearch.co.nz/Data/DatasetDetails/2370/10859

Carter (2014) 1 65

Pannell (2010) 41 36 186

Personal

communication

Broker, Gary (2010) 2

Carter, Di (2011) 13

Jackson, Jill (2010) 1

Rentoul, Sandy (2010) 1

Smith, Kathryn (2010) 1

Smith, Paula (2010) 2

Waghorn, Robin (2010) 7

*Including digitised and non-digitised specimens

http://data.gbif.org/

http://www.virtualherbarium.org/

139

Table B.2 Details of all numbered sites in Figure 3.1. “Use” distinguishes between weather stations

used for precipitation data (P), and field sites used for cuttings only (C), seeds only (S), or both (CS).

Longitude and latitude in decimal degrees (WGS 84), elevation in MASL. Aspect (cardinal direction)

and % overhead canopy cover (CC) measured at field sites only. Asterisks (*) denote sites where CC

is caused by trees (as opposed to low garden features at seed sites). “Precip.WS” indicates the weather

station used for precipitation data at each field site.

No. Site ID Use Full name Long. Lat. Elev. Aspect CC Precip.WS

1 AE P Akaroa EWS 172.9657 -43.8094 45 - - N/A

2 B1 CS Bowenvale 1 172.6551 -43.5816 239 S 0 CG

3 B2 C Bowenvale 2 172.6493 -43.5833 40 W 0 CG

4 B3 C Bowenvale 3 172.6519 -43.5878 67 W 0 CG

5 B4 C Bowenvale 4 172.6517 -43.5916 67 W 0 CG

6 B5 CS Bowenvale 5 172.6445 -43.6000 358 N 0 GB

7 B6 CS Bowenvale 6 172.6654 -43.5953 340 N 0 GB

8 BF1 CS Birdling's Flat 1 172.7182 -43.8141 8 N/A 0 MB

9 BF2 CS Birdling’s Flat 2 172.7197 -43.8126 7 N/A 0 MB

10 CG P Christchurch Gardens 172.6190 -43.5310 7 - - N/A

11 CK1 CS Coopers Knob 1 172.6236 -43.6532 477 W 0 LS

12 CK2 CS Coopers Knob 2 172.6233 -43.6551 471 N 0 LS


14 CK4 CS Coopers Knob 4 172.6236 -43.6584 532 N 0 LS


16 CK6 CS Coopers Knob 6 172.6240 -43.6653 479 W 32* LS

17 CP S CP (Lyttelton) 172.7149 -43.6011 60 S 97 LH

18 EW S EW (Cashmere) 172.6345 -43.5690 40 W 43 CG

19 FT S FT (Charteris Bay) 172.7136 -43.6386 35 N 20 LS

20 GB P Governor’s Bay 172.6504 -43.6278 274 - - N/A

21 GP1 CS Greenwood Park 1 172.7465 -43.5741 200 E 0 LH



24 GP4 CS Greenwood Park 4 172.7418 -43.5825 319 E 0 GB

25 GP5 CS Greenwood Park 5 172.7440 -43.5785 305 N 0 GB


27 GPWT S Greenwood Park Water Tanks 172.7372 -43.5856 370 N 0 LH

28 JK S JK (Huntsbury) 172.6537 -43.5664 80 W 62 CG

29 JN S JN (Church Bay) 172.7238 -43.6300 75 N 54 LS

30 LBBA P Le Bons Bay AWS 173.1190 -43.7460 236 - 42* N/A

31 LH P Lyttelton Harbour 172.7240 -43.6080 5 - - N/A

32 LS P Living Springs 172.6468 -43.6464 38 - - N/A

33 MB P Magnet Bay 172.7440 -43.8440 6 - - N/A

34 MP1 CS Misty Peaks 1 172.9696 -43.8226 153 N 42* AE

35 MP2 CS Misty Peaks 2 172.9703 -43.8222 148 W 56* AE

36 MP3 CS Misty Peaks 3 172.9709 -43.8348 516 S 0 AE

37 MP4 CS Misty Peaks 4 172.9722 -43.8472 642 E 0 LBBA

38 MP5 CS Misty Peaks 5 172.9825 -43.8228 527 W 0 AE

39 MP6 CS Misty Peaks 6 172.9989 -43.8326 653 N 0 LBBA

40 OK P Okuti 172.8096 -43.7895 61 - - N/A

41 RH S RH (Heathcote) 172.7127 -43.5784 40 N 32 LH

42 SH1 C Scarborough Hill 1 172.7524 -43.5871 78 W 0 LH

43 SH2 C Scarborough Hill 2 172.7610 -43.5879 295 E 0 LH

44 SH3 C Scarborough Hill 3 172.7678 -43.5936 180 E 0 LH

45 SH4 C Scarborough Hill 4 172.7693 -43.5932 180 S 0 LH

46 TO1 CS Te Oka 1 172.7883 -43.8379 130 E 60* MB

47 TO2 CS Te Oka 2 172.7864 -43.8454 60 E 0 MB

48 TO3 CS Te Oka 3 172.7749 -43.8578 39 E 0 MB

49 TO4 CS Te Oka 4 172.7718 -43.8569 38 W 0 MB

50 TO5 CS Te Oka 5 172.7743 -43.8502 61 W 0 MB

51 TO6 CS Te Oka 6 172.7760 -43.8361 316 E 0 MB

52 TO7 CS Te Oka 7 172.7845 -43.8238 483 E 0 OK

53 TO8 CS Te Oka 8 172.8169 -43.8133 681 E 0 OK

54 TO9 CS Te Oka 9 172.8228 -43.8158 616 W 0 OK

55 TO10 CS Te Oka 10 172.8202 -43.8225 567 W 0 OK

140

(a) (b) (c)

Figure B.2 Elevation (MASL) versus total annual precipitation (mm) on Banks Peninsula, taken from 30-arc-second Worldclim layers [(Hijmans et al. 2005),

available at http://www.worldclim.org]. Grey points show values for entire Peninsula, black points show values at recorded presence locations of a) Aeonium

arboreum b) A. haworthii and c) Cotyledon orbiculata.


141

Table B.3 Individual seed weight of Aeonium arboreum, A. haworthii and Cotyledon orbiculata, and

weight of seed and chaff estimated to contain 100 seeds, according to seed source site. Also given are

results of tetrazolium tests, as percentages of seeds found to be fully stained (viable, high vigour) and

pale stained (viable, low vigour).

Species Site

Seed

weight

(µg)

Content

weight 100

seeds (g)

Full

stain %

Pale

stain

%

Total

viable

%

A. arboreum

Church Bay 1 20 4.4 x 10-3

65 23 88

Church Bay 2 20 7.9 x 10-3

70 11 81

Hays Bay 1 20 5.7 x 10-3

57 25 82

Hays Bay 2 20 2.3 x 10-2

49 28 77

Lyttelton 1 20 6.8 x 10-3

55 39 94

Lyttelton 2 20 1.4 x 10-2

51 31 82

Sumner 1 20 3.9 x 10-3

52 30 82

Sumner 2 20 4.0 x 10-3

56 24 80

A. haworthii

Camp Bay 1 26 4.7 x 10-3

42 37 79

Camp Bay 2 26 7.2 x 10-3

46 27 73

Church Bay 26 1.6 x 10-2

10 16 26

East Sumner 1 26 8.6 x 10-3

45 34 79

East Sumner 2 26 1.2 x 10-2

17 29 46

Hays Bay 26 7.0 x 10-3

48 26 74

Taylor’s Mistake 1 26 1.0 x 10-1

42 34 76

Taylor’s Mistake 2 26 5.4 x 10-3

44 29 73

C. orbiculata

Birdling’s Flat 1 29 3.6 x 10-3

35 34 69

Birdling’s Flat 2 29 4.0 x 10-3

34 19 53

Godley Head 1 29 4.6 x 10-3

45 40 85

Godley Head 2 29 2.9 x 10-3

53 37 90

Okains Bay 1 29 5.0 x 10-3

52 35 87

Okains Bay 2 29 5.0 x 10-3

43 31 74

Pigeon Bay 1 29 5.1 x 10-3

51 46 97

Pigeon Bay 2 29 7.4 x 10-3

47 41 88

142

Figure B.3 Cotyledon orbiculata seeds under microscope at 100 × magnification. Seeds have been

stained with TTC and seed coat removed. Top row show pale and partial staining and are non-viable

due to necrosis of vital tissue. Middle row show full staining indicating viability and high vigour.

Bottom row show no staining and are completely non-viable.

143

Figure B.4 Scatterplots showing similar relationships between relative growth, calculated as

[ln (Volumet+1) – ln (Volumet)], and annual frost days and elevation, in both years of field experiment.

Year one indicated by black points, year two by red points. Shown for Aeonium arboreum (a, b)

A. haworthii (c, d) and Cotyledon orbiculata (e, f).

144

Figure B.5 Correlations of elevation with five annual climatic variables (a-e) at field transplant sites,

over both years. Seed tray only sites not used due to incomplete year one data. Only one year of data

presented for solar radiation (e) due to negligible differences between years. Pearson’s correlation

coefficient (r) and statistical significance indicated in figures, by * (p < 0.05), ** (p < 0.01), or

*** (p < 0.001).

145

(a) (b) (c)

(d) (e) (f)

Figure B.6 Canopy volume (L) at previous measurement interval of a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata, grouped by survival.

Relationship between mean canopy volume, cumulative frost days and % deaths per site, of d) A. arboreum, e) A. haworthii and f) C. orbiculata.

146

(a) (b) (c)

Figure B.7 Canopy volume required for 50% survival at a given elevation, in years 1 and 2, according to final models for a) Aeonium arboreum, b) A. haworthii and

c) Cotyledon orbiculata. Predictions generated along a hypothetical gradient where frost increases linearly with elevation, and shade is set to zero.

147

Appendix C - Supporting information for Chapter 4

C.1 Road survey methodology

A presence/absence survey of Aeonium arboreum, A. haworthii and Cotyledon orbiculata was

conducted on Banks Peninsula in 2010. I aimed to cover as much as the region as possible,

encompassing a representative sample of all habitats and land use types. It was bounded by the end of

Kaitorete spit in the West (- 43.856, 172.378 decimal degrees WGS 1984), Mount Pleasant in the

North (- 43.555, 172.715), Le Bons Bay in the East (- 43.742, 173.102) and Waihuakina Bay in the

South (- 43.898, 172.947). Surveys took place between January and April 2010, covering 844 grid

cells of 30 arc-seconds (approximately 39% of the Peninsula’s total area). I focussed in particular on

areas pre-selected as likely to contain Crassulaceae or suitable habitat, based on species traits. Likely

habitat included rocky outcrops, roadsides, sea-facing cliffs and areas close to population centres. I

surveyed all bays, headlands and areas containing large rocky outcrops, as much as was accessible by

road or foot and feasible within the time. To maximise efficiency over the large study area, surveys

were conducted primarily along roadsides, driving slowly and stopping when A. arboreum,

A. haworthii or C. orbiculata were seen. I recorded the species, GPS co-ordinates and estimated

population size on the commonly used DAFOR scale (Dominant, Abundant, Frequent, Occasional,

and Rare). Where road access was not possible, public walking tracks were used. I also surveyed some

sea-facing cliffs by boat. All major roads, bays and likely presence locations were covered. Despite the

inherent bias of road surveys, this method was used as all three species are often found on roadside

cuttings, where surrounding dense vegetation or forest may be unsuitable. To minimise bias I took

care to survey the main habitat types found in the region: grazing land, reserves, native and exotic

forest, residential areas and seashore. I also covered a range of elevations between 0 and 800 MASL,

aiming to survey as many rock outcrops as possible. A prior vegetation survey of all rock outcrops

above 500 MASL on Banks Peninsula found no exotic Crassulaceae (Wiser & Buxton 2009), thus

outcrops above 500 MASL were excluded and I focussed mainly on lower elevations. The resulting

presence/absence data was combined with pre-existing occurrence data collected from external sources

(Table B.1, total 32 additional grid cells) to map the species’ distributions on Banks Peninsula and to

select survey sites.

148

C.2 Supporting data

Figure C.1 All 30 arc-second cells surveyed for Aeonium arboreum, A. haworthii and Cotyledon orbiculata on Banks Peninsula, b) extent indicator.

149

Figure C.2 Maps of populations of a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata

on Banks Peninsula. Inset maps show New Zealand presences of each species. Points on Banks

Peninsula scaled by population size (Abundant = extensive, constant; Frequent = extensive, scattered;

Occasional = few, scattered; Rare = one individual). Red points indicate accessible populations, black

points inaccessible (e.g. cliffs). Road centrelines shown in dark grey.

150

Figure C.3 Elevation vs. annual precipitation gradient across Banks Peninsula (grey), and at known populations of a) Aeonium arboreum, b) A haworthii and

c) Cotyledon orbiculata (black), and at sites chosen for surveys (red). Precipitation data taken from 30 arc-second Worldclim layer [(Hijmans et al. 2005), available

at http://www.worldclim.org/bioclim].

A B C

http://www.worldclim.org/bioclim

151

Table C.1 Details of Aeonium arboreum, A. haworthii and Cotyledon orbiculata survey sites. Longitude and latitude given in decimal degrees (WGS 1984),

elevation in MASL, aspect to the nearest cardinal point. Habitat and earthquake (EQ) damage are visual assessments, geological units from G.N.S. Science (2014).

Categories of EQ damage are none, rock fall (RF) or landslides (LS), divided into small (S), moderate (M) and large (L).

Species Site ID Latitude Longitude Elevation Aspect Geological Unit Habitat EQ

Damage

A. arboreum

Church Bay 1 CHB1 -43.6344 172.7230 61 W Diamond Harbour Volcanics Inland cliffs, exotic shrubs RF (M)

Church Bay 2 CHB2 -43.6342 172.7207 43 N Diamond Harbour Volcanics Roadside loess, exotic shrubs LS (S)

Hays Bay 1 HB1 -43.6364 172.7155 27 N Allandale Rhyolite Roadside loess, exotic shrubs None

Hays Bay 2 HB2 -43.6400 172.7129 17 W Allandale Rhyolite Roadside loess, exotic shrubs None

Lyttelton Beach LB -43.6101 172.7034 0 W Governors Bay Andesite Coastal cliffs, exotic shrubs RF (S)

Lyttelton Car Park LCP -43.6101 172.7041 8 S Governors Bay Andesite Coastal cliffs, exotic shrubs RF (L)

North Sumner NS -43.5739 172.7582 18 E Lyttelton Volcanics Inland cliffs, exotic shrubs RF (L)

South Sumner SS -43.5745 172.7579 15 E Lyttelton Volcanics Inland cliffs, exotic shrubs RF (M)

A. haworthii

Camp Bay 1 CAB1 -43.6226 172.7820 3 N Lyttelton Volcanics Coastal cliffs, sparse vegetation None

Camp Bay 2 CAB2 -43.6221 172.7834 14 N Lyttelton Volcanics Coastal clifftop, under pine None

Church Bay CHB -43.6348 172.7229 61 W Diamond Harbour Volcanics Inland cliffs, exotic shrubs RF (M)

East Sumner Lifeboat ESL -43.5720 172.7715 13 W Lyttelton Volcanics Coastal cliffs, exotic shrubs RF (M)

East Sumner Wading Pool ESWP -43.5740 172.7699 20 W Lyttelton Volcanics Inland cliffs, exotic shrubs RF (M)

Hays Bay HB -43.6383 172.7143 26 W Allandale Rhyolite Roadside loess, exotic shrubs None

Taylors Mistake Beach TMB -43.5850 172.7781 17 W Lyttelton Volcanics Coastal loess, sparse tussock None

Taylors Mistake Roadside TMR -43.5801 172.7750 19 E Lyttelton Volcanics Roadside loess, exotic shrubs None

C. orbiculata

Birdlings Flat 1 BF1 -43.8260 172.7013 4 NA Holocene Shoreline Deposit Beach shingle, exotic shrubs None

Birdlings Flat 2 BF2 -43.8253 172.7053 8 NA Holocene Shoreline Deposit Beach shingle, depleted grass None

Godley Head 1 GH1 -43.5845 172.7795 21 N Lyttelton Volcanics Coastal loess, grazed tussock LS (S)

Godley Head 2 GH2 -43.5869 172.7841 32 N Lyttelton Volcanics Coastal loess, grazed tussock LS (S)

Okains Bay 1 OB1 -43.6958 173.0690 27 W Akaroa Volcanics Coastal cliffs, sparse vegetation None

Okains Bay 2 OB2 -43.6975 173.0628 17 W Akaroa Volcanics Coastal cliffs and grassland None

Pigeon Bay 1 PB1 -43.6490 172.9167 14 E Akaroa Volcanics Coastal loess, grazed tussock None

Pigeon Bay 2 PB2 -43.6788 172.8900 39 W Mid Pleistocene Loess Roadside loess, under pine None

152

Table C.2 Life stage categories used in surveys of Aeonium arboreum, A. haworthii and Cotyledon

orbiculata on Banks Peninsula.

Life stage A. arboreum A. haworthii C. orbiculata

Seedling ≤ one order of branching,

stems not woody

< 5 cm tall, or if greater, no

branching

< 10 cm tall, no branching,

leaves < 4 cm long

Juvenile ≥ one order of branching,

thick woody stems, no

evidence of flowering

≥ two orders of branching,

> 5 cm tall, no evidence of

flowering

> 10 cm tall, one order of

branching, large leaves, no

evidence of flowering

Adult

(not

flowering)

Previous years’

inflorescences visible or

multi branched and

> 30 cm tall

Previous years’


fully developed into dense

subshrub

Previous years’


multi branched with fully

formed leaves

Adult

(flowering)

New inflorescences visible New inflorescences visible New inflorescences visible

Figure C.4 Map of weather stations on Banks Peninsula (n = 8, dark blue points) with precipitation

data for 2010 - 2012, the time period of flowering surveys. Survey sites (n = 24) shown as green

points, all points labelled by site or station name, roads indicated by grey lines. Weather station data

available from CliFlo (National Institute of Water and Atmospheric Research 2014).

153

Figure C.5 Histograms of a) annual growing degree days base 5 (GDD5), b) annual precipitation

(mm), and c) annual solar radiation (KWh/M2), at survey sites of all three target species. Data shown

for both years of surveys. Temperature data taken from site data loggers, precipitation from the nearest

weather station, and solar radiation modelled in ArcMap 10.1.

A B C

154

Figure C.6 Mosaic plots (a-c) and boxplots (d-l) of measured reproductive traits at survey sites in

2012. Columns, from left to right: Aeonium arboreum, A. haworthii and Cotyledon orbiculata. Rows,

from top to bottom: proportion of all plants flowering (black) and not flowering (grey) with thickness

of bars scaled to sample size; and on flowering plants, inflorescences per plant; flowers per

inflorescence; seeds per pod. Survey sites ordered by increasing GDD10, shown for each site (m-o).

155

Appendix D- Supporting information for Chapter 5

Table D.1 List of all point locations for which IPMs were run. Type denotes whether site is a weather

station (WS; data available at http://cliflo.niwa.co.nz/), or a field experiment (FE) or survey site (FS;

see Chapter 3 and Chapter 4). Longitude and latitude in decimal degrees (WGS 1984), elevation in

MASL. Precip.WS denotes the ID of the weather station used for precipitation values for each site,

also available through CliFlo, * denotes weather stations used for precipitation data only not listed in

table, full names given below table. Species present indicates which species (Aeonium arboreum,

A. haworthii, Cotyledon orbiculata) are present within the same 30-arc-second grid cell as the site.

Site ID Type Full name Long. Lat. Elev. Precip.WS Species

present

AE WS Akaroa EWS 172.9657 -43.8094 45 AE Aa Ah Co

B1 FE Bowenvale 1 172.6551 -43.5816 239 CG -

B2 FE Bowenvale 2 172.6493 -43.5833 40 CG -

B3 FE Bowenvale 3 172.6519 -43.5878 67 CG -

B4 FE Bowenvale 4 172.6517 -43.5916 67 CG -

B5 FE Bowenvale 5 172.6445 -43.6000 358 GB* -

B6 FE Bowenvale 6 172.6654 -43.5953 340 GB* -

BF1 FE Birdlings Flat 1 172.7182 -43.8141 8 MB* -

BF1_S FS Birdlings Flat 1 Survey 172.7043 -43.8261 4 MB* Aa Ah Co

BF2 FE Birdlings Flat 2 172.7197 -43.8126 7 MB* -

BF2_S FS Birdlings Flat 2 Survey 172.7053 -43.8254 8 MB* Aa Ah Co

CA WS Christhurch Aero 172.5370 -43.4930 37 CA -

CAB1 FS Camp Bay 1 172.7835 -43.6220 3 LH Ah Co

CAB2 FS Camp Bay 2 172.7852 -43.6219 14 LH Ah Co

CG WS Christchurch Gardens 172.6190 -43.5310 7 CG -

CHB FS Church Bay 172.7230 -43.6344 61 LS* Aa Ah Co

CHB1 FS Church Bay 1 172.7230 -43.6344 61 LS* Aa Ah Co

CHB2 FS Church Bay 2 172.7212 -43.6343 43 LS* Aa Ah Co

CK1 FE Coopers Knob 1 172.6236 -43.6532 477 LS* -






CKSE WS Christchurch Kyle St EWS 172.6077 -43.5307 6 CKSE Ah

CNBP WS Christchurch New Brighton Pier 172.7350 -43.5060 12 CG Aa Ah Co

CP FE CP (Lyttelton) 172.7149 -43.6011 60 LH Aa Ah Co

ESL FS East Sumner Lifeboat 172.7711 -43.5724 13 CG Aa Ah Co

ESWP FS East Sumner Wading Pool 172.7698 -43.5740 20 CG Aa Ah Co

EW FE EW (Cashmere) 172.6345 -43.5690 40 CG Aa Ah

FT FE FT (Charteris Bay) 172.7136 -43.6386 35 LS* Aa Ah Co

GH1 FS Godley Head 1 172.7787 -43.5847 21 CG Aa Ah Co

GH2 FS Godley Head 2 172.7837 -43.5866 32 CG Aa Ah Co

GP1 FE Greenwood Park 1 172.7465 -43.5741 200 LH -

GP2 FE Greenwood Park 2 172.7527 -43.5776 167 LH Aa Ah Co

GP3 FE Greenwood Park 3 172.7403 -43.5936 234 LH -

GP4 FE Greenwood Park 4 172.7418 -43.5825 319 GB* Co

GP5 FE Greenwood Park 5 172.7440 -43.5785 305 GB* -

GP6 FE Greenwood Park 6 172.7445 -43.5884 285 LH Co

GPWT FE Greenwood Park Water Tanks 172.7372 -43.5856 370 LH Co

HB FS Hays Bay 172.7145 -43.6376 26 LS* Aa Ah Co

HB1 FS Hays Bay 1 172.7154 -43.6363 27 LS* Aa Ah Co

HB2 FS Hays Bay 2 172.7136 -43.6388 17 LS* Aa Ah Co

JK FE JK (Huntsbury) 172.6537 -43.5664 80 CG Aa Ah

JN FE JN (Church Bay) 172.7238 -43.6300 75 LS* Aa Ah Co


156

LB FS Lyttelton Beach 172.7032 -43.6101 0 LH Aa Ah

LBBA WS Le Bons Bay AWS 173.1190 -43.7460 236 LBBA Co

LBE WS Lincoln Broadfield EWS 172.4704 -43.6262 18 LBE Co

LCP FS Lyttelton Car Park 172.7037 -43.6103 8 LH Aa Ah

LH WS Lyttelton Harbour 172.7240 -43.6080 5 LH Aa Ah Co

LHCC WS Leeston Harts Creek CWS 172.3116 -43.7894 12 LHCC -

LR WS Leeston RAWS 172.3049 -43.7615 15 LR Co

MP1 FE Misty Peaks 1 172.9696 -43.8226 153 AE -



MP4 FE Misty Peaks 4 172.9722 -43.8472 642 LBBA -


MP6 FE Misty Peaks 6 172.9989 -43.8326 653 LBBA -

NS FS North Sumner 172.7585 -43.5736 18 CG Aa Ah Co

OB1 FS Okains Bay 1 173.0695 -43.6959 27 LBBA Co

OB2 FS Okains Bay 2 173.0644 -43.6970 17 LBBA Co

PB1 FS Pigeon Bay 1 172.8913 -43.6822 14 LBBA Co

PB2 FS Pigeon Bay 2 172.9153 -43.6571 39 LBBA Co

RE WS Rangiora EWS 172.6111 -43.3286 23 RE -

RH FE RH (Heathcote) 172.7127 -43.5784 40 LH -

SH1 FE Scarborough Hill 1 172.7524 -43.5871 78 LH Ah Co

SH2 FE Scarborough Hill 2 172.7610 -43.5879 295 LH Co



SLA WS Sugar Loaf AWS 172.6490 -43.6050 466 GB* -

SS FS South Sumner 172.7583 -43.5745 15 CG Aa Ah Co

TMB FS Taylors Mistake Beach 172.7783 -43.5848 17 CG Aa Ah Co

TMR FS Taylors Mistake Road 172.7747 -43.5831 19 CG Aa Ah Co

TO1 FE Te Oka 1 172.7883 -43.8379 130 MB* -

TO2 FE Te Oka 2 172.7864 -43.8454 60 MB* -

TO3 FE Te Oka 3 172.7749 -43.8578 39 MB* -

TO4 FE Te Oka 4 172.7718 -43.8569 38 MB* -

TO5 FE Te Oka 5 172.7743 -43.8502 61 MB* -

TO6 FE Te Oka 6 172.7760 -43.8361 316 MB* -

TO7 FE Te Oka 7 172.7845 -43.8238 483 OK* -

TO8 FE Te Oka 8 172.8169 -43.8133 681 OK* -

TO9 FE Te Oka 9 172.8228 -43.8158 616 OK* -

TO10 FE Te Oka 10 172.8202 -43.8225 567 OK* -

* GB = Governors Bay; MB = Magnet Bay; LS = Living Springs; OK = Okuti

157

Figure D.1 Annual frost days, GDD10 and GDD5 from 1992-2012, at weather stations used as IPM

locations (see Table D.1 for abbreviations)

Table D.2 Paired t-test results for mean annual frost days, GDD5 and GDD10 at weather stations used

as IPM locations. Results given for 2-year versus 5-year, 10-year and 20-year means, with degrees of

freedom (DF), t and p-values. Significant results indicated in bold.

Variable Two vs Five Year Two vs Ten Year Two vs Twenty Year

DF t p DF t p DF t p

Frost 9 0.38 0.71 6 0.70 0.51 4 0.51 0.64

GDD5 9 3.23 0.01 6 0.86 0.42 4 - 0.94 0.40

GDD10 9 8.03 2 x 10-5

6 2.07 0.08 4 0.10 0.93

158

Figure D.2 a) Daily minimum and b) daily maximum temperatures, between December 2010 and

November 2011, at sites with data loggers (black) and at weather stations (red).

Table D.3 Minimum, mean and maximum correlations (r) between data logger sites and the nearest

weather station over 2011-2012. Minimum and maximum temperature rescaled as residuals of the site

sample mean before calculating correlation coefficient.

Temperature °C Minimum r Mean r Maximum r

Daily Minimum 0.56 0.85 0.92

Daily Maximum 0.38 0.54 0.67

A

B

159

Figure D.3 Structure of a Lefkovitch Matrix Model (size-structured). Lefkovitch matrices are

conceptually similar to IPMs. In this example, there are 5 size classes, 4 of which are reproductive,

and individuals may grow, shrink or stay the same size in each time step. Graphical representations of

the IPM results of these components are given in Figure D.4, Figure D.5 and Figure D.6 (the reader

should note that the matrices are transposed in the IPM, but the same concepts apply).

[ 𝑁0

𝑁1

𝑁2

𝑁3

𝑁4]

a) Population Vector

The initial population is given in a

vector, where each value is the

number of individuals in each size

class. In the IPM, this would have

length 1000, all with values being 0.

[ 𝑆0

𝑆1

𝑆2

𝑆3

𝑆4]

b) Survival Vector

The survival vector gives the probability

of an individual in each size class

surviving the time step. Applied to the

IPM, this would have 1000 values, each

one calculated by integrating the

survival kernel as a function of plant size

and site variables.

[ 𝑃0,0

𝑃0,1

𝑃0,2

𝑃0,3

𝑃0,4

𝑃1,0

𝑃1,1

𝑃1,2

𝑃1,3

𝑃1,4

𝑃2,0

𝑃2,1

𝑃2,2

𝑃2,3

𝑃2,4

𝑃3,0

𝑃3,1

𝑃3,2

𝑃3,3

𝑃3,4

𝑃4,0

𝑃4,1

𝑃4,2

𝑃4,3

𝑃4,4]

c) Growth Matrix

The growth matrix gives the probability of

an individual transitioning to another size

class in each time step (for example, the

probability of an individual of size 2

becoming size 3 is represented here by

P2,3. In the IPM, this is a matrix of 1000 x

1000 cells, with each cell value calculated

by integrating the growth kernel as a

function of plant size and site variables.

[ 00000

𝐹1,0

0000

𝐹2,0

𝐹2,1

000

𝐹3,0

𝐹3,1

𝐹3,2

00

𝐹4,0

𝐹4,1

𝐹4,2

00 ]

d) Fecundity Matrix

The fecundity matrix gives the number

of new individuals produced per

existing individuals in each size class In

this example, I have imagined that new

individuals produced in each time step

may vary in size between size classes 0

and 2, and size classes 1-4 can

reproduce. For example, the number of

new offspring of size 1 produced by an

individual of size 4 is given by F4,1. The

same applies to the IPM, where the

matrix measures 1000 x 1000 and cell

values are calculated by integrating the

fecundity kernel, along with the

minimum size & probability

distribution of new offspring.

160

Figure D.4 Growth matrices (left) and fecundity matrices (right) at climatically good sites (upper 95th

percentile of λ) for Aeonium arboreum (OB1; a, b), A. haworthii (LCP; c, d) and Cotyledon orbiculata

(LB; e, f). Unit of plant size is cm (approximately equal to height). Colours show transition

probabilities between size classes (growth matrices) and individual fecundity (fecundity matrices).

161

Figure D.5 Growth matrices (left) and fecundity matrices (right) at climatically poor sites (lower 95th

percentile of λ) for Aeonium arboreum (MP5; a, b), A. haworthii (TO8; c, d) and Cotyledon orbiculata

(TO8; e, f). Unit of plant size is cm (approximately equal to height). Colours show transition

probabilities between size classes (growth matrices) and individual fecundity (fecundity matrices).

162

Figure D.6 Stable size distributions (left) and probability of survival versus plant size (right) for IPMs

of Aeonium arboreum (a, b), A. haworthii (c, d) and Cotyledon orbiculata (e, f), at climatically “good”

and “poor” sites (upper and lower 95th percentiles of λ). Site ID indicated in legend, size classes based

on plant height (cm).

163

Figure D.7 Elasticity plots of IPM matrices at climatically good sites (left, upper 95th percentile of λ)

and poor sites (right, lower 95th percentile of λ) for Aeonium arboreum (a, b), A. haworthii (c, d) and

Cotyledon orbiculata (e, f). Plant size units are cm (height).

164

Figure D.8 Bootstrapped distributions (n=1000) of mean BIOCLIM scores at IPM locations where λ >1 (climate suitable) and <1 (climate unsuitable), for

a) Aeonium arboreum, b) A. haworthii and c) Cotyledon orbiculata.

Figure D.9 True skill statistic (TSS), under prediction rate (UPR), sensitivity and specificity of BIOCLIM projections assessed against IPM predictions and true

presences, after iterative raising of suitability threshold, for a) Aeonium arboreum, b) A. haworthii and Cotyledon orbiculata.

165

Appendix E - Herbicide trial results

E.1 Rationale

In November 2012, at the end of the field transplant experiment on Banks Peninsula (Chapter 3), all

field sites were sprayed with herbicide and left in place for six weeks. Plants were sprayed primarily to

minimize chance of escape and to comply with the requirements of the permission to propagate

C. orbiculata granted by MPI. However, there is no quantitative data on herbicide effectiveness

against Aeonium arboreum, A. haworthii or Cotyledon orbiculata, so although spraying may be an

option for future control of the species, time and resources are likely to be wasted trialling different

control options. To investigate, I tested the effectiveness of six different herbicides against the study

species. After six weeks, plant damage was assessed, plant material removed and sites re-sprayed with

the most affective of the six herbicides.

E.2 Methods

Each site was sprayed with one of the six herbicides commonly used by the Port Hills Rangers for

weed control. Base herbicides were Glyphosate 1% (Roundup); Picloram 0.6% (Grazon) and

Metsulfuron-Methyl 1% (Escort) in aqueous solution. Because it was possible that water-based

herbicides might fail to penetrate the waxy leaves of the study species, I trialled each herbicide with

and without additional penetrant (Pulse™ for Roundup, and Silmaxx™ for Escort and Grazon). I

assigned herbicides randomly to sites within bins of low, medium and high elevation, balancing

number of sample sizes between treatments. Each site was sprayed using a hand-held sprayer in dry

conditions, at a rate of 1 L solution per 4 m2. After 6 weeks, I returned and recorded mortality and

plant damage on a scale of 0 – 5 (Error! Reference source not found.), excluding plants that were

dead prior to spraying. Individuals were recorded as dead only if severe internal cellular damage was

found, as over the course of the experiment individuals had regenerated from dried stems.

Table E.1 Scale used for visual assessment of damage to Aeonium arboreum, A. haworthii and

Cotyledon orbiculata six weeks after herbicide treatment.

Score Description

0 No visible damage

1 Mild damage to leaf margins

2 Mild damage to whole plant, or severe damage to leaf margins

3 Moderate damage to whole plant

4 Severe damage to whole plant, or almost dead

5 Dead – severe internal cellular damage, no chance of recovery

166

E.3 Results

Figure E.1 Damage to Aeonium arboreum plants (0 = no damage, 5 = complete mortality, see Table

E.1) after spraying with Escort (E), Escort with Silmaxx (ES), Grazon (G), Grazon with Silmaxx (GS),

Roundup (R), and Roundup with Pulse (RP).

Figure E.2 Damage to Aeonium haworthii plants (0 = no damage, 5 = complete mortality, see Table



Figure E.3 Damage to Cotyledon orbiculata plants (0 = no damage, 5 = complete mortality, see Table



167

Site /

Herbicide

Before herbicide treatment After herbicide treatment

TO2 /

Escort

MP2 /

Escort

Silmaxx

B3 /

Grazon

TO7 /

Grazon

Silmaxx

168

B5 /

Roundup

SH4 /

Roundup

Pulse

Figure E.4 Examples of before and six weeks after herbicide treatment at selected field sites.

Commercial name of herbicide given in table, site names correspond to Table B.2.

E.4 Summary

Glyphosate (Roundup) was the most effective of the three base herbicides, causing severe damage or

complete mortality to the majority of plants in all three species. Addition of the penetrant Pulse

increased effectiveness of Glyphosate against A. haworthii. Grazon (Picloram) was also relatively

effective against A. haworthii, especially with the addition of Silmaxx, but was only lethal to minority

of A. arboreum and C. orbiculata plants. Escort had a very minor effect on plant health, though with

the addition of Silmaxx it was nearly as effective as Grazon against C. orbiculata. Based on these

results I tentatively recommend Glyphosate, with or without Pulse, for control of the three species.

However, it would be beneficial to repeat similar trials in wild populations.

169

Supplementary materials

S.1 - IPM coefficients

Table S.1 Coefficients used in IPMs of Aeonium arboreum, A. haworthii and Cotyledon orbiculata.

Coefficient Value

A. arboreum A. haworthii C. orbiculata

Summer Survival Intercept 0004.939 0004.335 0003.104

Summer Survival Slope (Volume t) --001.602 0002.224 0001.824

Summer Survival Slope (Elevation) 00 -1.424 00 -1.580

Winter Survival Intercept 0004.370 0003.039 0007.515

Winter Survival Slope (Volume t) 0004.013 0001.713 0001.633

Winter Survival Slope (Cumulative Frost) 00 -7.726 00 -8.185 0 -13.489

Growth Intercept 7479.518 3176.283 2711.492

Growth Slope (Elevation) -1802.254 -1213.649 -308.353

Growth Slope (Elevation2) -2615.438 -826.492

Growth Slope (Annual Frost) -1737.254

Growth Slope (Volume t) 0000.922 0000.413 0000.404

Growth SD 5 5 5

P[Flower] Intercept 0 0-4.100 00 -4.434 00 -0.257

P[Flower] Slope (Volume t) 0006.461 0007.669 0004.593

P[Flower] Slope (GDD10) 0000.802

P[Flower] Slope (Radiation) 0001.079

Germination Intercept 00 -7.983 00 -7.337 00 -9.346

Germination Slope (GDD5) 0001.111

Germination Slope (Annual Frost) 00 -2.913

Germination Slope (Annual Precipitation) 00 -1.329 00 -2.453

Germination Slope (Elevation) 00 -2.575

Establishment Probability 1 1 1

Recruit Size Mean 2 2 2

Recruit Size SD 1 1 1

Inflorescences per Plant Intercept 0001.360 0000.912 0001.151

Inflorescences per Plant Slope (Volume t) 0001.592

Flowers per Inflorescence Intercept 0005.707 0004.882 0004.029

Flowers per Inflorescence Slope (Volume t) 0001.593

Seeds per Pod Intercept 0002.654 0002.580 0007.202

Seeds per Pod Slope (Pods per Inflorescence) 0000.101 0001.617

170

S.2 - R code for IPMs, adapted from Merow, Dahlgren, et al. (2014)

### Read in parameters, variables and mean/sd log volumes ###

vols<-read.table(“mean_log_vols.txt”, header=T, sep=”\t”)

vols<-subset(vols, Species==”Species”)

attach(vols)

params<-read.table(“params.txt”, header=T, sep=”\t”) # coefficients

elevg<-read.table(“elev_growth.txt”, header=T, sep=”\t”) ## variables

############### define the matrix ####################

min.size=2 # minimum height observed

max.size=55 # maximum height observed

n=1000 # number of cells in matrix

b=min.size+c(0:n)*(max.size-min.size)/n # boundary points

y=0.5*(b[1:n]+b[2:(n+1)]) # mesh points

h=y[2]-y[1] # step size

Math.cbrt <- function(x) {

sign(x) * abs(x)^(1/3)

} # function for cube root for rescaling volume to height

############### run the matrix ####################

ld<-as.data.frame(setNames(replicate(83, numeric(1),simplify=F),

names(elevg))) # make empty lambda data frame

### create loop and run matrix for each site ###

## presented below for A. arboreum. For other species modify kernels ##

for(i in 1:83){

## survival kernel

s.x=function(x, params) {

us= exp(params$ssurv.int+params$ssurv.slopeE*elevs[,i]+

params$ssurv.slopeV*((log(x^3)-smlv)/sslv))

ssurv=us/(1+us) # summer survival

ws=exp(params$wsurv.int+params$wsurv.slopeV*((log(x^3)-wmlv)/wslv)+

params$wsurv.slopeF*cumfrost[,i])

wsurv=ws/(1+ws) # winter survival

return(ssurv*wsurv) # annual survival

}

## growth kernel

g.yx = function (xp, x, params) {

(dnorm(xp, mean=

Math.cbrt(params$growth.int+params$growth.slopeE*elevg[,i]+

params$growth.slopeE2*(elevg[,i]^2)+params$growth.slopeS*(x^3)),

sd=params$growth.sd))

} # calculate growth, translate back to height for matrix

## fecundity kernel step 1

# P(reproduce) flowering * germination probability

p.reproduce = function (x, params) {

(exp(params$pfl.int+params$pfl.slopeV*((log(x^3)-fmlv)/fslv)+

params$pfl.slopeG*gdd10[,i]))

/(1+(exp(params$pfl.int+params$pfl.slopeV*((log(x^3)-

fmlv)/fslv)+params$pfl.slopeG*gdd10[,i])))*

171

(exp(params$germ.int+params$germ.slopeG*gdd5[,i]+params$germ.slopeF*

annfrost[,i]+params$germ.slopeP*precip[,i]))

/(1+(exp(params$germ.int+params$germ.slopeG*gdd5[,i]

+params$germ.slopeF*annfrost[,i]+params$germ.slopeP*precip[,i])))

}

## final fecundity kernel

# p(reproduce) x seed output

f.yx<-function(xp,x, params) {

p.reproduce(x,params)*

params$establishment.prob*

dnorm(xp, mean=params$recruit.size.mean, sd=params$recruit.size.sd)*

exp(params$inf.pl.int)*exp(params$fl.inf.int)*

(exp(params$seed.int+params$seed.slopeP*((log(params$fl.inf)-sdmlv)/

sdslv)))

}

### apply kernels to matrix ###

G = h*outer(y,y,g.yx, params=params) # growth matrix

S = s.x(y, params=params) # survival matrix

Fc = h*outer(y,y,f.yx, params=params) # fecundity matrix

P=G # placeholder; redefine P on next line

for (j in 1:(n)) {

G[1,j]<-G[1,j]+1-sum(G[,j])

P[,j]<-G[,j]*S[j]

} # growth/survival matrix

K=P+Fc # full IPM matrix

### write lambdas ####

ld[,i]<-(lam=Re(eigen(K)$values[1]))

}

172

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